Two applications of twisted wreath products to finite soluble groups

Hawkes, Trevor O.

doi:10.1090/S0002-9947-1975-0379657-X

Two applications of twisted wreath products to finite soluble groups
HTML articles powered by AMS MathViewer

by Trevor O. Hawkes

Trans. Amer. Math. Soc. 214 (1975), 325-335

DOI: https://doi.org/10.1090/S0002-9947-1975-0379657-X

PDF | Request permission

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.

References

Roger Carter, Bernd Fischer, and Trevor Hawkes, Extreme classes of finite soluble groups, J. Algebra 9 (1968), 285–313. MR 228581, DOI 10.1016/0021-8693(68)90027-6
Roger Carter and Trevor Hawkes, The ${\cal F}$-normalizers of a finite soluble group, J. Algebra 5 (1967), 175–202. MR 206089, DOI 10.1016/0021-8693(67)90034-8
E. C. Dade, Carter subgroups and Fitting heights of finite solvable groups, Illinois J. Math. 13 (1969), 449–514. MR 255679
T. O. Hawkes, An example in the theory of soluble groups, Proc. Cambridge Philos. Soc. 67 (1970), 13–16. MR 248225, DOI 10.1017/s0305004100057030
T. O. Hawkes, The family of Schunck classes as a lattice, J. Algebra 39 (1976), no. 2, 527–550. MR 407134, DOI 10.1016/0021-8693(76)90051-X
B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703, DOI 10.1007/978-3-642-64981-3
Gary M. Seitz, Solvable groups having system normalizers of prime order, Trans. Amer. Math. Soc. 183 (1973), 165–173. MR 347970, DOI 10.1090/S0002-9947-1973-0347970-6

On system normalizers of prime order

John G. Thompson, Automorphisms of solvable groups, J. Algebra 1 (1964), 259–267. MR 173710, DOI 10.1016/0021-8693(64)90022-5