Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T23:35:52.597Z Has data issue: false hasContentIssue false
  • English
  • Français

The application of the principal ideal theorem to p-groups

Published online by Cambridge University Press:  22 January 2016

Katsuya Miyake
Katsuya Miyake*
Affiliation:
Department of Mathematics, College of General Education, Nagoya University, Chikusa-ku, Nagoya 464, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let p be a fixed prime integer, and G a finite p-group. For a subgroup H of G, we denote the centralizer of H in G by CG(H). The commutator subgroup of G is denoted by [G, G].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 99 , September 1985 , pp. 73 - 88
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 1 ] Alperin, J. and Tzee-Nan, Kuo, The exponent and the projective representations of a finite group, Illinois J. Math., 11 (1967), 410–414.Google Scholar
[ 2 ] Hall, P., A contribution to the theory of groups of prime power order, Proc. London Math. Soc, (2), 36 (1933), 29–95.Google Scholar
[ 3 ] Huppert, B., Endliche Gruppen I, Springer-Verlag, Berlin · Heidelberg · New York (1967).CrossRefGoogle Scholar
[ 4 ] Miyake, K., On the structure of the idele groups of algebraic number fields, II, Tôhoku Math. J., 34 (1982), 101–112.CrossRefGoogle Scholar
[ 5 ] Miyake, K., A generalization of Hubert’s Theorem 94, Nagoya Math. J., 96 (1984), 83–94.Google Scholar
[ 6 ] Terada, F., A principal ideal theorem in the genus field, Tôhoku Math. J., 23 (1971), 697–718.Google Scholar
[ 7 ] Zassenhaus, H., The theory of groups, 2 nd edit., Chelsea Pub. Co., New York (1958).Google Scholar