Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T00:02:12.181Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on A-Groups

Published online by Cambridge University Press:  22 January 2016

Noboru Itô
Noboru Itô*
Affiliation:
Mathematical Institute, Nagoya University
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 us consider soluble groups whose Sylow subgroups are all abelian. Such groups we call A-groups, following P. Hall. A-groups were investigated thoroughly by P. Hall and D. R. Taunt from the view point of the structure theory. In this note, we want to give some remarks concerning representation theoretical properties of A-groups.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 4 , June 1952 , pp. 79 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1952

References

1) Hall, P., The construction of soluble groups. J. Reine Angew. Math. 182, 206–214 (1940)Google Scholar.

D. R. Taunt, On A-groups. Proc. Cambridge Philos. Soc. 45, 24-42 (1949).

The latter is not yet accessible to me.

2) Blichfeld, H., Finite Collineation Groups. Chicago (1917)Google Scholar.

3) Tazawa, M., Über die monomial darstellbaren endlichen Substitutionsgruppen. Proc. Acad. Jap. 10, 397-398 (1934)CrossRefGoogle Scholar.

4) Taketa, K., Über die Gruppen, deren Darstellungen sich sämtlich auf monomiale Gestalt transformieren lassen. Proc. Acad. Jap. 6, 31-33 (1930)CrossRefGoogle Scholar.

5) Itô, N., On the characters of soluble groups. These Journal 3, 31-48 (1951)Google Scholar.

6) Brauer, R. and Nesbitt, C., On the modular characters of groups. Ann. Math. 42, 556-590 (1941)CrossRefGoogle Scholar.

7) Brauer, R., On the arithmetic in a group ring. Proc. Nat. Acad. Sci. U.S.A. 109-114 (1944)Google Scholar. N. Itô, Some studies on group characters. These Journal 2, 17-28 (1951). (A remark to my paper: It was evident that f/eKfK = 1 by a theorem of L Schur, from which the description can be rather shortened.)

8) N. Itô, On the degrees of irreducible representations of a finite group. These Journal 3, 5-6 (1951).