Benjamin Sambale

PD Dr. Benjamin Sambale

Welcome to my homepage!

I'm currently a Heisenberg fellow and a lecturer (Lehrbeauftragter)


Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Fakultät für Mathematik und Physik
Welfengarten 1, 30167 Hannover
Office: A451
Leibniz Universität Hannover


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  • Vita

    Recent positions

    • Present:  Heisenberg fellow and lecturer at LUH Hannover

    • 2019–2021:  Temporary associate professor at Hannover

    • 2018–2019: Temporary associate professor at FSU Jena

    • 2015–2018: Heisenberg fellow at TUK Kaiserslautern

    • 2013: Habilitation in Jena

    • 2012: PostDoc at UC Santa Cruz

    • 2010: PhD in Jena


    • Diploma thesis: Konjugationsklassen und Charaktere in endlichen p-Gruppenpdf
    • Dissertation: 2-Blöcke mit metazyklischen und minimal nichtabelschen Defektgruppenpdf
    • Habilitationsschrift: Blocks of finite groups and their invariantspdf, presentation slides (in German): pdf

    Research profiles

    I am not on ResearchGate (although they created an inaccurate account on my name).

    My Erdős number is 3 (via Isaacs-Diaconis)

    Editor: Jahresbericht DMV

  • Interests

    Mathematical interests

    • finite groups

    • characters and representations

    • blocks theory

    • permutation groups

    • fusion systems

    • finite-dimensional algebras

    If you find yourself sitting next to me at a conference dinner, the following may help to break the ice.

    Personal interests

    • running (formerly: basketball, skateboarding, juggling, gymnastics, climbing, slacklining)

    • piano (playing and recording)

    • arch linux

    • LaTeX

    • psychology

    • lucid dreaming

    • creative writing

    • sugarfree sustainable food

    My personal bests in running are:

    • 1.000m in 2:58min

    • 3.000m in 9:53min

    • 5.000m in 16:58min

    • 10.000m in 35:22min

    (all with spikes on track).

  • Teaching


    Recent courses

    Winter 21-22

    Sommer 21

    Winter 20-21

    Lecture notes (in German)

    Shorter Notes

    Supervised theses

    • Jonathan Gruber, Invariants of character tables of finite groups, Bachelorarbeit, TU Kaiserslautern, 2017
    • Christoph Lampe, On the Classification of p-Blocks of Finite Groups, Masterarbeit, TU Kaiserslautern, 2017
    • Robin Gießler, Gruppentheoretische Beweise von Menons Identität, Bachelorarbeit, FSU Jena, 2019
    • Lucas Büchner Mayench, Der Satz von Kulakoff-Hall, Bachelorarbeit, FSU Jena, 2019
    • Sophie Friesen, Der Satz von Poincaré-Birkhoff-Witt, Bachelorarbeit, LUH, 2020
    • Philipp Wellmann, Gruppenelemente maximaler Ordnung, Bachelorarbeit, LUH, 2021
    • Nadja van Kempen, Mathieupuzzle und Verallgemeinerungen, Masterarbeit, LUH, 2021
    • Julia Krivorutski, Permutationsgruppen mit regulären Bahnen, Bachelorarbeit, LUH, 2021
    • Karl Böhlke, Algorithmen zur Planarität von Graphen, Bachelorarbeit, LUH, 2021 (in preparation)
  • Publications



    Research articles:

    1. (with L. Héthelyi and B. Külshammer) Conjugacy classes and characters of finite p-groups, Comm. Algebra 39 (2011), 657–685, pdf
    2. Cartan matrices and Brauer's k(B)-conjecture, J. Algebra 331 (2011), 416–427, pdf
    3. Cartan matrices and Brauer's k(B)-conjecture II, J. Algebra 337 (2011), 345–362, pdf
    4. 2-Blocks with minimal nonabelian defect groups, J. Algebra 337 (2011), 261–284, pdf
    5. Fusion systems on metacyclic 2-groups, Osaka J. Math. 49 (2012), 325–329, pdf
    6. Blocks with defect group D2n × C2m , J. Pure Appl. Algebra 216 (2012), 119–125, pdf
    7. (with C. W. Eaton and B. Külshammer) 2-Blocks with minimal nonabelian defect groups II, J. Group Theory 15 (2012), 311–321, pdf
    8. (with B. Külshammer) The 2-blocks of defect 4, Represent. Theory 17 (2013), 226–236, pdf
    9. Brauer's Height Zero Conjecture for metacyclic defect groups, Pacific J. Math. 262 (2013), 481–507, pdf
    10. Blocks with central product defect group D2n ∗ C2m, Proc. Amer. Math. Soc. 141 (2013), 4057–4069, pdf
    11. Blocks with defect group Q2n × C2m and SD2n × C2m, Algebr. Represent. Theory 16 (2013), 1717–1732, pdf
    12. Further evidence for conjectures in block theory, Algebra Number Theory 7 (2013), 2241–2273, pdf
    13. (with L. Héthelyi and B. Külshammer) A note on Olsson's Conjecture, J. Algebra 398 (2014), 364–385, pdf
    14. (with C. W. Eaton, R. Kessar and B. Külshammer) 2-blocks with abelian defect groups, Adv. Math. 254 (2014), 706–735, pdf
    15. On the Brauer-Feit bound for abelian defect groups, Math. Z. 276 (2014), 785–797, pdf
    16. (with B. Külshammer, G. Navarro and P. H. Tiep) Finite groups with two conjugacy classes of p-elements and related questions for p-blocks, Bull. London Math. Soc. 46 (2014), 305–314, pdf
    17. (with S. Koshitani and B. Külshammer) On Loewy lengths of blocks, Math. Proc. Cambridge Philos. Soc. 156 (2014), 555–570, pdf
    18. Exponent and p-rank of finite p-groups and applications, Arch. Math. (Basel) 103 (2014), 11–20, pdf
    19. (with L. Héthelyi, R. Kessar and B. Külshammer) Blocks with transitive fusion systems, J. Algebra 424 (2015), 190–207, pdf
    20. Cartan matrices and Brauer's k(B)-Conjecture III, Manuscripta Math. 146 (2015), 505–518, pdf
    21. The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups, Proc. Amer. Math. Soc. 143 (2015), 4291–4304, pdf
    22. Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups, Internat. J. Algebra Comput. 25 (2015), 951–976, pdf
    23. 2-Blocks with minimal nonabelian defect groups III, Pacific J. Math. 280 (2016), 475–487, pdf
    24. Fusion systems on bicyclic 2-groups, Proc. Edinb. Math. Soc. 59 (2016), 989–1018, pdf
    25. (with P. Landrock) On centers of blocks with one simple module, J. Algebra 472 (2017), 339–368, pdf
    26. On blocks with abelian defect groups of small rank, Results Math. 71 (2017), 411–422, pdf
    27. (with G. Navarro) A counterexample to Feit's Problem VIII on decomposition numbers, J. Algebra 477 (2017), 494–495, pdf
    28. Cartan matrices and Brauer's k(B)-Conjecture IV, J. Math. Soc. Japan 69 (2017), 735–754, pdf
    29. Isotypies for the quasisimple groups with exceptional Schur multiplier, J. Algebra Appl. 16 (2017), 1750078, pdf
    30. On a theorem of Blichfeldt, Expo. Math. 35 (2017), 221–255, pdf
    31. Refinements of the orthogonality relations for blocks, Algebr. Represent. Theory 20 (2017), 1109–1131, pdf
    32. (with G. Malle and G. Navarro) On defects of characters and decomposition numbers, Algebra Number Theory 11 (2017), 1357–1384, pdf
    33. A counterexample to a conjecture of Wada, J. Algebra 489 (2017), 582–585, pdf
    34. Regular orbits of coprime linear groups in large characteristic, Bull. Aust. Math. Soc. 96 (2017), 438–444, pdf
    35. (with G. Navarro and P. H. Tiep) Characters and Sylow 2-subgroups of maximal class revisited, J. Pure Appl. Algebra 222 (2018), 3721–3732, pdf
    36. Solution of Brauer's k(B)-Conjecture for pi-blocks of pi-separable groups, Forum Math. 30 (2018), 1061–1064, pdf
    37. (with A. Bächle) Groups whose elements are not conjugate to their powers, Arch. Math. 110 (2018), 447–454, pdf
    38. (with G. Navarro) On the blockwise modular isomorphism problem, Manuscripta Math. 157 (2018), 263–278, pdf
    39. (with B. Külshammer) Loewy lengths of centers of blocks, Q. J. Math. 69 (2018), 855–870, pdf
    40. Remarks on Harada's Conjecture, Israel J. Math. 228 (2018), 513–526, pdf
    41. Morita equivalent blocks of symmetric groups, SIGMA 14 (2018), 100, 8 pages, pdfGAP code for Conjecture 1, GAP code for Conjecture 2, Magma code for Conjecture 2
    42. On the projective height zero conjecture, Proc. Amer. Math. Soc. 147 (2019), 487–488, pdf
    43. Pseudo Sylow numbers, Amer. Math. Monthly 126 (2019), 60–65, pdf
    44. (with B. Külshammer and Y. Otokita) Loewy lengths of centers of blocks II, Nagoya Math. J. 234 (2019), 127–138, pdf
    45. Pseudo Frobenius numbers, Expo. Math. 37 (2019), 200–206, pdf
    46. Bounding the number of characters in a block of a finite group, Adv. Math. 358 (2019), 106861, 20 pp. pdf
    47. (with I. M. Isaacs and G. Navarro) Irreducible extensions of characters, Israel J. Math. 234 (2019), 629–644, pdf
    48. Landau's Theorem for pi-blocks of pi-separable groups, appears in Adv. Group Theory Appl. 8 (2019), 103–115, pdf
    49. (with A. Bächle) Orders generated by character values, Monatsh. Math. 191 (2020), 665–678, pdf
    50. (with E. Giannelli) On restriction of characters to defect groups, J. Algebra 558 (2020), 423–433, pdf
    51. Character tables and defect groups, J. Algebra 562 (2020), 323–340, pdf
    52. (with E. Giannelli, N. Rizo and A. A. Schaeffer Fry) Groups with few p'-characters degrees in the principal block, Proc. Amer. Math. Soc. 148 (2020), 4597–4614, pdf
    53. On a theorem of Ledermann and Neumann, Amer. Math. Monthly 127 (2020), 827–834, pdf
    54. Survey on perfect isometries, Rocky Mountain J. Math. 50 (2020), 1517–1539, pdf
    55. (with G. Navarro) Weights and nilpotent subgroups, Int. Math. Res. Not. 2021 (2021), 2526–2538, pdf
    56. Blocks with small-dimensional basic algebra, Bull. Aust. Math. Soc., 103 (2021), 461–474, pdf
    57. Generalized bases of finite groups, Arch. Math. 117 (2021), 9–18, pdf
    58. The reciprocal character of the conjugation action, Publ. Math. Debrecen 99 (2021), 243–260, pdf
    59. (with D. Rossi) Restrictions of characters in p-solvable groups, J. Algebra 587 (2021), 130–141, pdf
    60. (with C. G. Ardito) Broué's Conjecture for 2-blocks with elementary abelian defect groups of order 32, appears in Adv. Group Theory Appl., pdf
    61. (with S. Koshitani and C. Lassueur) Splendid Morita equivalences for principal blocks with semidihedral defect groups, to appear in Proc. Amer. Math. Soc., pdf
    62. (with M. Tărnăuceanu) On the size of coset unions, appears in J. Algebraic Combin.
    63. (with P. Wellmann) On a bound of Cocke and Venkataraman, appears in Monatsh. Math., pdfsmall group ids
    64. (with C. G. Ardito) Cartan matrices and Brauer's k(B)-Conjecture V, submitted, pdf (under review since Nov 2019…)
    65. (with N. N. Hung and P. H. Tiep) Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements, submitted, pdf
    66. (with G. Navarro) Alternating sums over pi-subgroups, submitted, pdf


    Some of my papers are also on arXiv.

    If you find any mistakes/typos please let me know.

  • Talks


    Disclaimer: I prefer blackboard talks whenever possible. 

    Slides and videos of talks

    • Aachen 2010: Cartan matrices and Brauer's k(B)-conjecturepdf
    • Copenhagen 2011: Block theory and fusion systemspdf
    • Hannover 2011: New inequalities concerning Olsson's Conjecturepdf
    • Aachen 2011: Donovan's Conjecture for certain defect groupspdf
    • Oberwolfach 2012: Survey on invariants of blocks of finite groupspdf
    • Oberwolfach research report 2012: pdf
    • Saarbrücken 2012: Further evidence for conjectures in block theorypdf
    • Bad Boll 2013: On Loewy lengths of blockspdf
    • Manchester 2013: On the Brauer-Feit bound for abelian defect groupspdf
    • Banff 2014: The Alperin-McKay Conjecture for a special class of defect groupspdfVideo link
    • Jena 2015: Cartan matrices and Brauer's k(B)-Conjecturepdf
    • Maynooth 2016: Orthogonality relations for characters and blockspdf
    • Jena 2016: Orthogonality relations for characters and blocks (different talk), pdf
    • Banff 2017: On the blockwise modular isomorphism problemVideo
    • Berkeley 2018: 5-Minute talkpdfVideo
    • Berkeley 2018: Fusion systems of groups and blockspdf
    • Berkeley 2018: Characters and Sylow 2-subgroups of maximal classVideo

    A longer list including my blackboard talks is part of my CV.

  • Miscellaneous


    Useful links:
    Literature resources

    Computer algebra systems

    Tables and data bases

    Homepages, blogs, listings

    Jobs and societies

    Good reads:

    A Magma bug:
    reported in July 2017, still present in version V2.26-8 (can be checked with the online calculator)

    A0:=BasicAlgebraOfBlockAlgebra([ProjectiveModule(A,i):i in bl[1]]);
    A0:=BasicAlgebraOfBlockAlgebra([ProjectiveModule(A,i):i in bl[1]]);
    A0:=BasicAlgebraOfBlockAlgebra([PIM[i]:i in bl[1]]);


    (correct answer is 46)