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Critical group
In
mathematics
, in
the realm
of
group theory
, a
group
is said to be
critical
if it is not in the
variety
generated by all its
proper
subquotients, which includes all its
subgroups
and all its
quotients
.
Any
finite
monolithic
A-group
is critical. This result is due to
Kovacs
and
Newman
.
The variety generated by a
finite group
has a
finite number
of nonisomorphic critical
groups
.
