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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A group-theoretic characterization of $M$-groups
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by Alan E. Parks
Proc. Amer. Math. Soc. 94 (1985), 209-212
DOI: https://doi.org/10.1090/S0002-9939-1985-0784164-8

Abstract:

Groups having the property that all their complex irreducible characters are monomial are characterized in terms of the embedding of cyclic sections of the group.
References
  • T. R. Berger, Representation theory and solvable groups: length type problems, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 431–441. MR 604618
  • Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
  • B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703, DOI 10.1007/978-3-642-64981-3
  • I. Martin Isaacs, Character theory of finite groups, Pure and Applied Mathematics, No. 69, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0460423
  • I. Martin Isaacs, Primitive characters, normal subgroups, and $M$-groups, Math. Z. 177 (1981), no. 2, 267–284. MR 612879, DOI 10.1007/BF01214205
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Bibliographic Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 209-212
  • MSC: Primary 20C15; Secondary 20D10
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0784164-8
  • MathSciNet review: 784164