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
DOI:
https://doi.org/10.1090/S0002-9947-1975-0379657-X
MathSciNet review:
0379657
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Abstract | References | Similar Articles | Additional Information
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.
- [1] Roger Carter, Bernd Fischer, and Trevor Hawkes, Extreme classes of finite soluble groups, J. Algebra 9 (1968), 285–313. MR 0228581, https://doi.org/10.1016/0021-8693(68)90027-6
- [2] Roger Carter and Trevor Hawkes, The \cal𝐹-normalizers of a finite soluble group, J. Algebra 5 (1967), 175–202. MR 0206089, https://doi.org/10.1016/0021-8693(67)90034-8
- [3] E. C. Dade, Carter subgroups and Fitting heights of finite solvable groups, Illinois J. Math. 13 (1969), 449–514. MR 0255679
- [4] T. O. Hawkes, An example in the theory of soluble groups, Proc. Cambridge Philos. Soc. 67 (1970), 13–16. MR 0248225
- [5] T. O. Hawkes, The family of Schunck classes as a lattice, J. Algebra 39 (1976), no. 2, 527–550. MR 0407134, https://doi.org/10.1016/0021-8693(76)90051-X
- [6] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
- [7] Gary M. Seitz, Solvable groups having system normalizers of prime order, Trans. Amer. Math. Soc. 183 (1973), 165–173. MR 0347970, https://doi.org/10.1090/S0002-9947-1973-0347970-6
- [8] G. M. Seitz, On system normalizers of prime order, University of Oregon (preprint).
- [9] John G. Thompson, Automorphisms of solvable groups, J. Algebra 1 (1964), 259–267. MR 0173710, https://doi.org/10.1016/0021-8693(64)90022-5
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1975-0379657-X
Keywords:
Twisted wreath product,
nilpotent length,
Clifford theory,
primitive group,
Carter subgroup
Article copyright:
© Copyright 1975
American Mathematical Society