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HALL SUBGROUPS AND -COCYCLE REGULARITY
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Journal Article
HALL SUBGROUPS AND -COCYCLE REGULARITY
2024
Overview
Let
H
be a subgroup of a finite group
G
and let
$\\alpha $
be a complex-valued
$2$
-cocycle of
$G.$
Conditions are found to ensure there exists a nontrivial element of
H
that is
$\\alpha $
-regular in
$G.$
However, a new result is established allowing a prime by prime analysis of the Sylow subgroups of
$C_G(x)$
to determine the
$\\alpha $
-regularity of a given
$x\\in G.$
In particular, this result implies that every
$\\alpha _H$
-regular element of a normal Hall subgroup
H
is
$\\alpha $
-regular in
$G.$
Publisher
Cambridge University Press
Subject
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