P-stable linear representation

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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 G be a finite group and p be an odd prime number. Suppose \rho:G \to GL(V) is a linear representation of G over a finite field of characteristic p. We say that \rho is p-stable if for no non-identity p-element g of G (i.e., an element whose order is a power of p) does \rho(g) 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