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

Zvi Arad

Vol. 62 (1976), No. 1, 29–35

DOI: 10.2140/pjm.1976.62.29

Abstract

Denote the maximum of the orders of all nilpotent subgroups A of class at most c, of a finite group G, by d_c(G). Let A_c(G) be the set of all nilpotent subgroups of class at most c and having order d_c(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