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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Subgroups of finite soluble groups inducing
the same permutation character


Author: Norberto Gavioli
Journal: Trans. Amer. Math. Soc. 349 (1997), 2969-2980
MSC (1991): Primary {20C99, 20D10}
MathSciNet review: 1370642
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Abstract: In this paper there are found necessary and sufficient conditions that a pair of solvable finite groups, say $G$ and $K$, must satisfy for the existence of a solvable finite group $L$ containing two isomorphic copies of $G$ and $H$ inducing the same permutation character. Also a construction of $L$ is given as an iterated wreath product, with respect to their actions on their natural modules, of finite one-dimensional affine groups.


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Additional Information

Norberto Gavioli
Affiliation: Dipartimento di Matematica Pura ed Applicata, Università de L’Aquila, via Vetoio, I-67010 Coppito (AQ), Italy
Email: gavioli@univaq.it

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01696-6
PII: S 0002-9947(97)01696-6
Keywords: Permutation character of finite groups, finite solvable groups
Received by editor(s): October 7, 1994
Received by editor(s) in revised form: January 4, 1996
Additional Notes: Work partially supported by M.U.R.S.T
Article copyright: © Copyright 1997 American Mathematical Society