1. Finite Groups with Submultiplicative Spectra
- Author
-
Grunenfelder, L., Košir, T., Omladič, M., and Radjavi, H.
- Subjects
Mathematics - Group Theory ,15A30, 20C15, 20D15 (Primary) 15A18, 20E10 (Secondary) - Abstract
We study abstract finite groups with the property, called property $\hat{s}$, that all of their subrepresentations have submultiplicative spectra. Such groups are necessarily nilpotent and we focus on $p$-groups. $p$-groups with property $\hat{s}$ are regular. Hence, a 2-group has property $\hat{s}$ if and only if it is commutative. For an odd prime $p$, all $p$-abelian groups have property $\hat{s}$, in particular all groups of exponent $p$ have it. We show that a 3-group or a metabelian $p$-group ($p \ge 5$) has property $\hat{s}$ if and only if it is V-regular.
- Published
- 2011