Vol. 62, No. 1, 1976

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

Zvi Arad

Vol. 62 (1976), No. 1, 29–35
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). Let Ac(G) be the set of all nilpotent subgroups of class at most c and having order dc(G) in G. Let A(G) denote the set of all nilpotent subgroups of maximal order of a group G.

The aim of this paper is to investigate the set A(G) of groups G of odd order and the structure of the groups G with the property A2(G) A(G). Theorem 1 gives an expression for the number of elements in A(G). Theorem 2 gives criteria for the nilpotency of groups of odd order.

Mathematical Subject Classification 2000
Primary: 20D25
Milestones
Received: 26 September 1974
Revised: 30 October 1975
Published: 1 January 1976
Authors
Zvi Arad