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

Zvi Arad
1976 Pacific Journal of Mathematics  
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 ΰ (G) in G. Let Λoc(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 Λ=c(G) of groups G of odd order and the structure of the groups G with the property A 2 (G) C Λ^(G). Theorem 1 gives an expression for the number of
more » ... r the number of elements in Λoo(G). Theorem 2 gives criteria for the nilpotency of groups of odd order.
doi:10.2140/pjm.1976.62.29 fatcat:ggawwjmvdzahlbu5vwuxfc5hoi