Signalizer functor

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, in the area of <a href="/facts/Abstract_algebra/YNNE1CNz">abstract algebra</a>, a signalizer <a href="/facts/Functor/l2u3rIBE">functor</a> is a mapping from a potential <a href="/facts/Subgroup/r91mBgpa">finite subgroup</a> to the <a href="/facts/Centralizer_and_normalizer/AKhrEUGR">centralizers</a> of the nontrivial elements of an <a href="/facts/Abelian_group/FfWwmx4R">abelian group</a>. The signalizer functor theorem provides the conditions under which the source of such a functor is in fact a subgroup. 
</p><p>The signalizer functor was first defined by <a href="/facts/Daniel_Gorenstein/tBgFlDpt">Daniel Gorenstein</a>. <a href="/facts/George_Glauberman/PotfDt5q">George Glauberman</a> proved the Solvable Signalizer Functor Theorem for <a href="/facts/Solvable_group/Na7lKIns">solvable groups</a> and Patrick McBride proved it for general groups. Results concerning signalizer functors play a major role in the <a href="/facts/Classification_of_finite_simple_groups/nMwLJf1K">classification of finite simple groups</a>.
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Signalizer functor open-in-new

Signalizer functor