Vol. 62, No. 1, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
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