No CrossRef data available.
Article contents
A Theorem on Factorizable Groups of Odd Order
Published online by Cambridge University Press: 22 January 2016
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.
Recently, W. Feit [2] obtained some results on factorizable groups of odd order. By using his procedure and applying the theory of R. Brauer [1], we can prove the following theorem similar to that of W. Feit [2]:
Theorem. Let G be a factorizable group of odd order such that
G = HM
where H is a subgroup of order 3p, p being a prime greater than 3, and M is a maximal subgroup of G. Then G contains a proper normal subgroup which is contained either in H or in M.
- Type
- Research Article
- Information
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 1962
References
[1]
Brauer, R.: On permutation groups of prime degree and related classe of groups, Ann. of Math. 44, 44–57 (1943).Google Scholar
[2]
Feit, W.: A theorem of factorizable groups, Proc. Amer. Math. Soc. 11, 11–658 (1960).Google Scholar
[3]
Ikuta, T.: Über die Nichteinfachheit einer faktorisierbaren Gruppe, Nat. Sci. Rep. Lib. Arts Fac. Shizuoka Univ. 9, 9–1 (1956).Google Scholar
[4]
Nagai, O.: On transitive groups that contain non-abelian regular subgroups, Osaka Math. J. 13, 13–199 (1961).Google Scholar
[5]
Tuan, H.: On groups whose orders contain a prime number to the first power, Ann. of Math. 45, 45–110 (1944).Google Scholar
[6]
Wielandt, H.: Vorlesung über Permutationsgruppen (Ausarbeitung von J. André.)
Tübingen
1955.Google Scholar
You have
Access