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On the Characters of Soluble Groups

Published online by Cambridge University Press:  22 January 2016

Noboru Itô
Noboru Itô*
Affiliation:
Mathematical Institute, Nagoya University
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The theory of representations of finite groups, which was originated by G. Frobenius, has been developed by I. Schur to become popular and studied more and more profoundly by R. Brauer even in the current stage of modern algebra. However, it seems that its applications to the structure theory of finite groups are still far from being satisfactory, partially because these two theories for structure and for representation are not firmly tied up.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 3 , October 1951 , pp. 31 - 48
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1951

References

1) Schur, I., Neue Begründung der Theorie der Gruppencharaktere, Sitz. Berlin (1905), pp. 406–432.Google Scholar

2) Brauer, R. and Nesbitt, C., On the modular representations of groups of finite order I, Univ. Toronto studies Math. Series 4 (1937), pp. 20.Google Scholar

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

4) See 3).

5) Osima, M., On primary decomposable group rings, Proc. Phys.-Math. Soc. Japan 24 (1942), pp. 1–9.Google Scholar

6) Brauer, R., On the arithmetic in a group ring, Proc. Nat. Acad. Sci. U.S.A. (1944), pp. 109–114.CrossRefGoogle Scholar

7) See 5).

8) Hall, P., A note on soluble groups, Jour. London Math. Soc., 3 (1928), pp. 98–105.CrossRefGoogle Scholar

9) Zassenhaus, H., Über endliche Fastkörper, Hbg. Abh. 11 (1935), pp. 187–220.CrossRefGoogle Scholar

10) Shoda, K., Über direkt zerlegbare Gruppen, Jour. Fac. Sci., Tokyo 2 (1930).Google Scholar

11) Schur, I., Arithmetische Untersuchungen über endliche Gruppen lineare Substitutionen, Sitz. Berlin (1906), pp. 164–184.Google Scholar

12) Brauer, R., On Artin’s L-series with general group characters, Ann. Math. 48 (1947), pp. 502–514.CrossRefGoogle Scholar

13) See 11).

14) Frobenius, G., Über Relationen zwischen den Charakteren einer Gruppen und denen ihrer Untergruppen, Sitz. Berlin (1898), pp. 501–515.Google Scholar

15) Azumaya, G., Elementary proof of a theorem in number theory, Z-S-S-D. 1187 (1944), pp. 189–196 (in Japanese).Google Scholar

Chevalley, C., Sur la théorie du corps de classes dans les corps finis et les corps locaux, Jour. Coll. Sci., Tokyo 2 (1933), pp. 365–476.Google Scholar

16) Nakayama, T., Finite groups with faithful irreducible and directly indecomposable modular representations, Proc. Acad. Japan 23 (1947), pp. 22–25.CrossRefGoogle Scholar

17) See 5).

18) R. Brauer, On a conjecture by Nakayama, Trans. R. S. of Canada (1947).

19) H. Zassenhaus, Lehrbuch der Gruppentheorie I, (1937).

20) See 16).

21) See 3).

22) See 6).

23) See 3).

24) See 6).

25) Itô, N., Some studies on group characters, Nagoya Math. J. 2 (1951), pp. 17–28.CrossRefGoogle Scholar

26) See 6).

27) See 6).