Critical group

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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.

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