Conjugacy class sizes in arithmetic progression

Mariagrazia Bianchi, Stephen P. Glasby, Cheryl E. Praeger

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
2 Downloads (Pure)

Abstract

Let cs(G) denote the set of conjugacy class sizes of a group G, and let cs ∗ (G) = cs(G)\{1} be the sizes of non-central classes. We prove three results. We classify all finite groups for which (1) cs (G) = {a, a + d, ⋯, a + r d} is an arithmetic progression with r ≥ 2 (2) cs ∗ (G) = { 2, 4, 6 } (G)= {2,4,6} is the smallest case where cs ∗ (G) is an arithmetic progression of length more than 2 (our most substantial result); (3) the largest two members of cs ∗ (G) are coprime. For (3), it is not obvious, but it is true that cs ∗(G) has two elements, and so is an arithmetic progression.

Original languageEnglish
Pages (from-to)1039–1056
JournalJournal of Group Theory
Volume23
Issue number6
DOIs
Publication statusPublished - 2020

Fingerprint

Dive into the research topics of 'Conjugacy class sizes in arithmetic progression'. Together they form a unique fingerprint.

Cite this