Abelian and nilpotent subgroups of maximal order of groups of odd order

Zvi Arad

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Denote the maximum of the orders of all nilpotent subgroups A of class at most c, of a finite group G, by dc(G). LetAc (G) be the set of all nilpotent subgroups of class at most c andhaving order dc(G) in G. Let A(G) denote the set of allnilpotent subgroups of maximal order of a group G.The aim of this paper is to investigate the set A(G) ofgroups G of odd order and the structure of the groups G withthe property A2(G) ⊆ A(G). Theorem 1 gives an expressionfor the number of elements in A(G). Theorem 2 gives criteriafor the nilpotency of groups of odd order.

Original languageEnglish
Pages (from-to)29-35
Number of pages7
JournalPacific Journal of Mathematics
Volume62
Issue number1
DOIs
StatePublished - Jan 1976

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