P-stable linear representation
From Groupprops
This article describes a property to be evaluated for a linear representation of a group, i.e. a homomorphism from the group to the general linear group of a vector space over a field
Definition
Let be a finite group and be an odd prime number. Suppose is a linear representation of over a finite field of characteristic . We say that is -stable if for no non-identity -element of (i.e., an element whose order is a power of ) does satisfy a quadratic minimal polynomial.
References
Textbook references
- Finite Groups by Daniel Gorenstein, ISBN 0821843427, Page 103, Theorem 8.1, Chapter 3 (Representations of groups), Section 3.8 (p-stable representations), ^{More info}