Inseparable finite solvable groups

Bechtell, Homer

doi:10.1090/S0002-9947-1976-0427469-1

Inseparable finite solvable groups
HTML articles powered by AMS MathViewer

by Homer Bechtell PDF

Trans. Amer. Math. Soc. 216 (1976), 47-60 Request permission

Abstract:

A finite group is called inseparable if the only proper normal subgroup over which it splits is the identity element. The E-residual, for the formation E of groups in which all Sylow subgroups are elementary abelian, appears to control the action of splitting. In this article, inseparable solvable groups are identified that have a metacyclic Fitting subgroup and the E-residual a p-group.

References

Homer Bechtell, Elementary groups, Trans. Amer. Math. Soc. 114 (1965), 355–362. MR 175967, DOI 10.1090/S0002-9947-1965-0175967-3
Homer Bechtell, The theory of groups, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1971. MR 0284490
Homer Bechtell, On the structure of solvable $nC$-groups, Rend. Sem. Mat. Univ. Padova 47 (1972), 13–22. MR 323900
Ja. G. Berkovi, A generalization of theorems of P. Hall and N. Blackburn and their application to nonregular $p$-groups, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 800–830 (Russian). MR 0294495
C. Christensen, Groups with complemented normal subgroups, J. London Math. Soc. 42 (1967), 208–216. MR 207834, DOI 10.1112/jlms/s1-42.1.208
Wolfgang Gaschütz, Praefrattinigruppen, Arch. Math. (Basel) 13 (1962), 418–426 (German). MR 146262, DOI 10.1007/BF01650090
Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
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

The theory of groups