Abstract
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.
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This paper collects the results from the author’s master thesis [6], which she wrote at Leiden University under the supervision of Prof. Hendrik Lenstra. The author is very thankful to the referee for numerous helpful suggestions.
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Stanojkovski, M. Evolving groups. Arch. Math. 111, 3–12 (2018). https://doi.org/10.1007/s00013-018-1178-9
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DOI: https://doi.org/10.1007/s00013-018-1178-9