Vol. 31, No. 1, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Centralizers of abelian, normal subgroups of hypercyclic groups

Ulrich F. K. Schoenwaelder

Vol. 31 (1969), No. 1, 197–208

J. L. Alperin proved the following theorem about finite p-groups G: if E is maximal among the abelian, normal subgroups of G of exponent dividing pn, then ΩnC𝜃(E) = E, provided that pn2. It turns out that the restriction to p-groups and also to finite groups in Alperin’s proof is not essential. In fact a similar theorem holds in a large class of hypercyclic groups (Theorem 2.2). By the same method also a modified version (Theorem 2.8) will be obtained, the word “normal” in the assumptions about E being replaced by “characteristic”, here G is supposed to be hypercentral; the modification results in enlarging E to a characteristic subgroup k𝜃(E) of class 2 in a very definite way before taking its centralizer.

Mathematical Subject Classification
Primary: 20.40
Received: 18 November 1968
Published: 1 October 1969
Ulrich F. K. Schoenwaelder