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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Hall subgroups of $M$-groups need not be $M$-groups

Author(s): Hiroshi Fukushima
Journal: Proc. Amer. Math. Soc. 133 (2005), 671-675.
MSC (2000): Primary 20C15
Posted: August 24, 2004
MathSciNet review: 2113913
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Abstract | References | Similar articles | Additional information

Abstract: In this paper, we shall give examples of $M$-groups that have Hall subgroups that are not $M$-groups.

References:

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E.C.Dade. Normal subgroups of $M$-groups need not be $M$-groups. Math. Z. 133(1973), 313-317. MR 0325748 (48:4094)

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E.C.Dade. Monomial characters and normal subgroups. Math. Z. 178(1981), 401-420. MR 0635210 (83e:20014)

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L.Dornhoff. $M$-groups and $2$-groups. Math. Z. 100(1967), 226-256. MR 0217174 (36:265)

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I.M.Isaacs. Character theory of finite groups. Academic Press, San Diego, California, 1976. MR 0460423 (57:417)

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I.M. Isaacs, Primitive characters, normal subgroups, and $M$-groups, Math. Z. 177(1981), 267-284. MR 0612879 (82f:20026)

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R.W.Van der Waall. On the embedding of minimal non-$M$-groups. Indag. Math. 36(1974), 157-167. MR 0352237 (50:4724)

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Additional Information:

Hiroshi Fukushima
Affiliation: Department of Mathematics, Faculty of Education, Gunma University Maebashi, Gunma 371-8510, Japan
Email: fukusima@edu.gunma-u.ac.jp

DOI: 10.1090/S0002-9939-04-07645-2
PII: S 0002-9939(04)07645-2
Received by editor(s): June 23, 2003
Received by editor(s) in revised form: October 29, 2003
Posted: August 24, 2004
Communicated by: Jonathan I. Hall
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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