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The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups are characterized as semidirect products of two nilpotent groups of coprime orders where the action of one on the other is via automorphisms that map each subgroup to a conjugate.
KeywordsCohomology Tate groups Finite groups Evolving groups Intense automorphisms
Mathematics Subject Classification12G05 20D20 20E34 20F16
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- 4.M. Isaacs, Finite Group Theory, Graduate Studies in Mathematics, 92, American Mathematical Society, Providence, RI, 2008.Google Scholar
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