A group

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In mathematics, in the field of group theory, an A group is a finite group with the property that all its Sylow subgroups are abelian. The following can be said about A groups:

  • Every abelian group is an A group.
  • A nilpotent group is an A group if and only if it is abelian.
  • All the groups in the variety generated by a finite group are finitely approximable if and only if that group is an A group.
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