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

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
Received: 26 September 1974
Revised: 30 October 1975
Published: 1 January 1976
Zvi Arad