Description:
<p>The order of a Sylow <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2">
<mml:semantics>
<mml:mn>2</mml:mn>
<mml:annotation encoding="application/x-tex">2</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-subgroup of a multiplier group of an abelian Singer group is at most half the order of the order of a Sylow <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2">
<mml:semantics>
<mml:mn>2</mml:mn>
<mml:annotation encoding="application/x-tex">2</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-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 <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2">
<mml:semantics>
<mml:mn>2</mml:mn>
<mml:annotation encoding="application/x-tex">2</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-subgroup of a multiplier group on the structure of the Singer group.</p>