On the size of coset unions

authored by

Benjamin Sambale, Marius Tǎrnǎuceanu

Abstract

Let g₁H₁, … , g_nH_n be cosets of subgroups H₁, … , H_n of a finite group G such that g₁H₁∪ … ∪ g_nH_n≠ G. We prove that | g₁H₁∪ … ∪ g_nH_n| ≤ γ_n| G| where γ_n< 1 is a constant depending only on n. In special cases, we show that γ_n= (2 ⁿ- 1) / 2 ⁿ is the best possible constant with this property and we conjecture that this is generally true.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Al. I. Cuza University

Type

Article

Journal

Journal of algebraic combinatorics

Volume

55

Pages

979-987

No. of pages

9

ISSN

0925-9899

Publication date

05.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory, Discrete Mathematics and Combinatorics

Electronic version(s)

https://doi.org/10.1007/s10801-021-01079-x (Access: Open)