Normal subgroups contained in the Frattini subgroup. II
HTML articles powered by AMS MathViewer
- by W. Mack Hill PDF
- Proc. Amer. Math. Soc. 53 (1975), 277-279 Request permission
Abstract:
If $p$ is an odd prime and $H$ is a $p$-group with a characteristic subgroup $K$ such that $|K| > |K \cap Z(H)| = p$, then $H$ cannot be a normal subgroup contained in the Frattini subgroup of any finite group $G$.References
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Robert L. Griess Jr., Automorphisms of extra special groups and nonvanishing degree $2$ cohomology, Pacific J. Math. 48 (1973), 403–422. MR 476878
- W. Mack Hill, Frattini subgroups of $p$-closed and $p$-supersolvable groups, Israel J. Math. 19 (1974), 208–211. MR 369525, DOI 10.1007/BF02757713 —, Extra-special normal $p$-subgroups, Notices Amer. Math. Soc. 21 (1974), A-526. Abstract #74T-A214.
- W. Mack Hill and Donald B. Parker, The nilpotence class of the Frattini subgroup, Israel J. Math. 15 (1973), 211–215. MR 322058, DOI 10.1007/BF02787567
- W. Mack Hill and Charles R. B. Wright, Normal subgroups contained in the Frattini subgroup, Proc. Amer. Math. Soc. 35 (1972), 413–415. MR 301094, DOI 10.1090/S0002-9939-1972-0301094-7
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
- David L. Winter, The automorphism group of an extraspecial $p$-group, Rocky Mountain J. Math. 2 (1972), no. 2, 159–168. MR 297859, DOI 10.1216/RMJ-1972-2-2-159
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 277-279
- MSC: Primary 20D25
- DOI: https://doi.org/10.1090/S0002-9939-1975-0390051-3
- MathSciNet review: 0390051