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Transactions of the American Mathematical Society
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 ``small'' relative to its nilpotent length.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0379657-X
PII: S 0002-9947(1975)0379657-X
Keywords: Twisted wreath product, nilpotent length, Clifford theory, primitive group, Carter subgroup
Article copyright: © Copyright 1975 American Mathematical Society