Some inequalities for the multiplicator of a finite group

Jones, Michael R.

doi:10.1090/S0002-9939-1973-0314975-6

Some inequalities for the multiplicator of a finite group
HTML articles powered by AMS MathViewer

by Michael R. Jones PDF

Proc. Amer. Math. Soc. 39 (1973), 450-456 Request permission

Abstract:

The paper is devoted to the derivation of certain upper and lower bounds for the multiplicator of a finite group. The lower bounds enable us to give a sufficient condition for a finite group to have nontrivial multiplicator.

References

W. Gaschütz, J. Neubüser, and Ti Yen, Über den Multiplikator von $p$-Gruppen, Math. Z. 100 (1967), 93–96 (German). MR 217181, DOI 10.1007/BF01110785
J. A. Green, On the number of automorphisms of a finite group, Proc. Roy. Soc. London Ser. A 237 (1956), 574–581. MR 81901, DOI 10.1098/rspa.1956.0198
B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
Michael R. Jones, Multiplicators of $p$-groups, Math. Z. 127 (1972), 165–166. MR 318304, DOI 10.1007/BF01112608
Roger C. Lyndon, The cohomology theory of group extensions, Duke Math. J. 15 (1948), 271–292. MR 25468
Peter M. Neumann, An enumeration theorem for finite groups, Quart. J. Math. Oxford Ser. (2) 20 (1969), 395–401. MR 254134, DOI 10.1093/qmath/20.1.395

Untersuchungen über die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen

132