Singer groups, an approach from a group of multipliers of even order

Abstract

The order of a Sylow 2 2 -subgroup of a multiplier group of an abelian Singer group is at most half the order of the order of a Sylow 2 2 -subgroup of the automorphism group of the Singer group. We determine the situation when equality occurs. We also study the effect of a nontrivial Sylow 2 2 -subgroup of a multiplier group on the structure of the Singer group.