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On Quasinormal Subgroups II

Published online by Cambridge University Press:  22 January 2016

W. E. Deskins
W. E. Deskins*
Affiliation:
Michigan State University East Lansing, Michigan U.S.A.
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A subgroup was defined by O. Ore to be quasinormal in a group if it permuted with all subgroups of the group, and he proved [5] that such a subgroup is subnormal (= subinvariant = accessible) in a finite group. Finite groups in which all subgroups are quasinormal were classified by K. Iwasawa [3], and more recently N. Ito and J. Szép [2] and the author [1] proved that a quasi-normal subgroup is an extension of a normal subgroup by a nilpotent group. Similar results were obtained by O. Kegel [4] and in [1] for subgroups which permute not necessarily with all subgroups but with those having some special property.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 231 - 237
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Deskins, W. E., On quasinormal subgroups of finite groups, Math. Zeit. 82, 125–132 (1963)..Google Scholar
[2] Ito, N. and Szép, J., Uber die Quasinormalieiler von endlichen Gruppen, Acta Sci. Math Szeged 23, 1681–70 (1962).Google Scholar
[3] Iwasawa, K., Uber die endlichen Gruppen und die Verbande ihren Untergruppen, J. Univ. Tokyo 43, 171–199 (1941).Google Scholar
[4] Kegel, O. H., Sylow-Gruppen und Subnormalteiler endlichen Gruppen, Math. Zeit. 78, 205–221 (1962).Google Scholar
[5] Ore, O., Contributions to the theory of groups, Duke Math. J. 5, 431–460 (1939).Google Scholar