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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Two applications of twisted wreath products to finite soluble groups

Author: Trevor O. Hawkes
Journal: Trans. Amer. Math. Soc. 214 (1975), 325-335
MSC: Primary 20D10
MathSciNet review: 0379657
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Abstract: The group construction sometimes known as the twisted wreath product is used here to answer two questions in the theory of finite, soluble groups: first to show that an arbitrary finite, soluble group may be embedded as a subgroup of a group whose upper nilpotent series is a chief series; second to construct an A-group whose Carter subgroup is β€œsmall” relative to its nilpotent length.

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Keywords: Twisted wreath product, nilpotent length, Clifford theory, primitive group, Carter subgroup
Article copyright: © Copyright 1975 American Mathematical Society