Some conjugacy classes in groups associated with the general linear groups. (English) Zbl 0995.20027

Darafsheh, M. R.

Algebras Groups Geom. 15, No. 2, 183-199 (1998).

Summary: Let \(q\) be a power of the prime number \(p\) and \(n\) be a natural number. If \(A\in\text{GL}_n(q)\), then \(\theta(A)=(A^t)^{-1}\) is an outer automorphism of \(\text{GL}_n(q)\) if \((n,q)\neq(2,2)\); where \(A^t\) denotes the transpose of the matrix \(A\). In this case we set \(G^+=\text{GL}_n(q)\cdot\langle\theta\rangle\) and our aim in this paper is to find the conjugacy classes of elements of order 2 and 4 in \(G^+-\text{GL}_n(Q)\).

MSC:

20G40	Linear algebraic groups over finite fields
20E45	Conjugacy classes for groups
20F28	Automorphism groups of groups

Keywords:

general linear groups; outer automorphisms; conjugacy classes