Splitting via Noncommutativity

Mark Lanning Lewis, Daria Lytkina, Viktor Danilovich Mazurov, Ali Reza Moghaddamfar

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be a nonabelian group and n a natural number. We say that G has a strict n-split decomposition if it can be partitioned as the disjoint union of an abelian subgroup A and n nonempty subsets B-1, B-2, . . . , B-n, such that vertical bar B-i vertical bar > 1 for each i and within each set B-i, no two distinct elements commute. We show that every finite nonabelian group has a strict n-split decomposition for some n. We classify all finite groups G, up to isomorphism, which have a strict n-split decomposition for n = 1, 2, 3. Finally, we show that for a nonabelian group G having a strict n-split decomposition, the index vertical bar G : A vertical bar is bounded by some function of n.

Original languageEnglish
Pages (from-to)1051-1082
Number of pages32
JournalTaiwanese Journal of Mathematics
Volume22
Issue number5
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • strict n-split decomposition
  • simple group
  • commuting graph
  • Commuting graph
  • Simple group
  • Strict n-split decomposition

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