Some subgroups of symmetric groups determined using signed Brauer diagrams

Abstract

A class of subgroups of order [Formula: see text], [Formula: see text] [Formula: see text] of even permutations is obtained for symmetric group [Formula: see text] using the set [Formula: see text] of signed Brauer diagrams. Consequently, every group of order [Formula: see text] has a Sylow [Formula: see text]-subgroup of order [Formula: see text].