Strongly closed subgroup
From Groupprops
This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.
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Contents
Definition
Definition with symbols
Let be groups. Then,
is said to be strongly closed in
with respect to
if any
-conjugate of an element of
, which lies inside
, in fact lies inside
. In other words, for any
:
.
The term is typically used for the situation where is a Sylow subgroup of
. The particular case can also be generalized to the notion of a strongly closed subgroup for a fusion system.