The Frattini argument and $t$-groups
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- by Ben Brewster and Surinder Sehgal
- Proc. Amer. Math. Soc. 101 (1987), 239-245
- DOI: https://doi.org/10.1090/S0002-9939-1987-0902535-5
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Abstract:
If enough subgroups of a group satisfy the Frattini argument in the group, then normality is a transitive relation within the group. Subgroup functors are used to specify what enough is.References
- Donald W. Barnes and Otto H. Kegel, Gaschütz functors on finite soluble groups, Math. Z. 94 (1966), 134–142. MR 204511, DOI 10.1007/BF01118976
- James C. Beidleman, Ben Brewster, and Peter Hauck, Fittingfunktoren in endlichen auflösbaren Gruppen. I, Math. Z. 182 (1983), no. 3, 359–384 (German). MR 696533, DOI 10.1007/BF01179756
- James C. Beidleman, Ben Brewster, and Peter Hauck, Fitting functors in finite solvable groups. II, Math. Proc. Cambridge Philos. Soc. 101 (1987), no. 1, 37–55. MR 877699, DOI 10.1017/S0305004100066391
- Graham A. Chambers, $p$-normally embedded subgroups of finite soluble groups, J. Algebra 16 (1970), 442–455. MR 268275, DOI 10.1016/0021-8693(70)90018-9
- Wolfgang Gaschütz, Gruppen, in denen das Normalteilersein transitiv ist, J. Reine Angew. Math. 198 (1957), 87–92 (German). MR 91277, DOI 10.1515/crll.1957.198.87
- T. A. Peng, Finite groups with pro-normal subgroups, Proc. Amer. Math. Soc. 20 (1969), 232–234. MR 232850, DOI 10.1090/S0002-9939-1969-0232850-1
- Derek J. S. Robinson, A note on finite groups in which normality is transitive, Proc. Amer. Math. Soc. 19 (1968), 933–937. MR 230808, DOI 10.1090/S0002-9939-1968-0230808-9
- Derek J. S. Robinson, Groups which are minimal with respect to normality being intransitive, Pacific J. Math. 31 (1969), 777–785. MR 258943, DOI 10.2140/pjm.1969.31.777
- Derek John Scott Robinson, A course in the theory of groups, Graduate Texts in Mathematics, vol. 80, Springer-Verlag, New York-Berlin, 1982. MR 648604, DOI 10.1007/978-1-4684-0128-8
- Willi Sudbrock, Sylowfunktionen in endlichen Gruppen, Rend. Sem. Mat. Univ. Padova 36 (1966), 158–184 (German). MR 202828
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 239-245
- MSC: Primary 20D10
- DOI: https://doi.org/10.1090/S0002-9939-1987-0902535-5
- MathSciNet review: 902535