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The Strong -Sylow Theorem for the Groups PSL
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Journal Article
The Strong -Sylow Theorem for the Groups PSL
2024
Overview
Let
be a set of primes. A finite group
is a
-group if all prime divisors of the order of
belong to
. Following Wielandt, the
-Sylow theorem holds for
if all maximal
-subgroups of
are conjugate; if the
-Sylow theorem holds for every subgroup of
then the strong
-Sylow theorem holds for
. The strong
-Sylow theorem is known to hold for
if and only if it holds for every nonabelian composition factor of
. In 1979, Wielandt asked which finite simple nonabelian groups obey the strong
-Sylow theorem. By now the answer is known for sporadic and alternating groups. We give some arithmetic criterion for the validity of the strong
-Sylow theorem for the groups
.
Publisher
Pleiades Publishing,Springer Nature B.V
Subject
