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 language | English |
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Pages (from-to) | 29-35 |
Number of pages | 7 |
Journal | Pacific Journal of Mathematics |
Volume | 62 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1976 |