Vol. 53, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
The non-minimality of induced central representations

David Lee Wright

Vol. 53 (1974), No. 1, 301–306
Abstract

Let G be a finite p-group and G a minimal faithful permutation representation of G possessing the minimal number of generators of the centre of G transitive constituents. One surmises that the induced representation, G, of the centre of G, is minimal. The conjecture is validated subject to either of the hypotheses |G|pf except G = Q8 × Z1 or Z(G)n copies of the cyclic group of order pm and is trivial when G is abelian. However, a group of order p6 shows the conjecture to be false for p odd, also. The converse problem of extending minimal representations of Z(G) to minimal representations of G is also, in general, not possible.

Mathematical Subject Classification 2000
Primary: 20C15
Milestones
Received: 12 June 1973
Published: 1 July 1974
Authors
David Lee Wright