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An extension of Gow's theorem

Robert M. Guralnick, Pham Huu Tiep

Abstract

We extend Gow's theorem on products of semisimple regular conjugacy classes to finite groups whose generalized Fitting subgroup is Z(G)S where S is a quasisimple group of Lie type in characteristic p and Z(G) has order prime to p.

An extension of Gow's theorem

Abstract

We extend Gow's theorem on products of semisimple regular conjugacy classes to finite groups whose generalized Fitting subgroup is Z(G)S where S is a quasisimple group of Lie type in characteristic p and Z(G) has order prime to p.
Paper Structure (8 theorems, 38 equations)

This paper contains 8 theorems, 38 equations.

Key Result

Corollary 1

Let $G$ be as above. Assume that $a \in G$ has order prime to $p$, $|\mathbf{C}_S(a)|$ has order prime to $p$ and that $s \in S \smallsetminus \mathbf{Z}(S)$ is semisimple. Then $s^t = [a,u]$ for some $t, u \in S$.

Theorems & Definitions (16)

  • Corollary 1
  • Proposition 2
  • proof
  • Lemma 3
  • proof
  • Proposition 4
  • proof
  • Proposition 5
  • proof
  • Theorem 6
  • ...and 6 more