#### Title

A semi-recursion for the number of involutions in special orthogonal groups over finite fields

#### Document Type

Article

#### Department/Program

Mathematics

#### Journal Title

Finite Fields and Their Applications

#### Pub Date

2011

#### Volume

17

#### Issue

6

#### First Page

532

#### Abstract

Let I(n) be the number of involutions in a special orthogonal group SO(n,F-q) defined over a finite field with q elements, where q is the power of an odd prime. Then the numbers 1(n) form a semi-recursion, in that for m > 1 we have I(2m + 3) = (q(2m+2) + 1)I(2m + 1) + q(2m)(q(2m) - 1)I(2m - 2). We give a purely combinatorial proof of this result, and we apply it to give a universal bound for the character degree sum for finite classical groups defined over F-q. (C) 2011 Elsevier Inc. All rights reserved.

#### Recommended Citation

Vinroot, C. Ryan and Jiang, Feiqi, A semi-recursion for the number of involutions in special orthogonal groups over finite fields (2011). *Finite Fields and Their Applications*, 17(6), 532-551.

10.1016/j.ffa.2011.03.002

#### DOI

10.1016/j.ffa.2011.03.002