Skip to main content
Log in

On a generalization of monomial groups

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

We study a class of finite groups, called almost monomial groups, which generalize the class of monomial groups and is connected with the theory of Artin L-functions. Our method of research is based on finding similarities with the theory of monomial groups, whenever it is possible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Data availability

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

References

  1. Artin, E.: Zur Theorie der L-Reihen mit allgemeinen Gruppencharakteren. Abh. Math. Sem. Hamburg 8, 292–306 (1931)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bakshi, G.K., Maheshwary, S.: Extremely strong Shoda pairs with GAP. J. Symb. Comput. 76, 97–106 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Booker, A.R.: Artin’s conjecture, Turing’s method, and the Riemann hypothesis. Exp. Math. 15(4), 385–407 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Cimpoeaş, M.: On the semigroup ring of holomorphic Artin L-functions. Colloq. Math. 160(2), 283–295 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cimpoeaş, M., Nicolae, F.: Independence of Artin L-functions. Forum Math. 31(2), 529–534 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cimpoeaş, M., Nicolae, F.: Artin L-functions to almost monomial Galois groups. Forum Math. 32(4), 937–940 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen, Kwang-Wu.: On relative M-groups. Chin. J. Math. 21(1), 1–12 (1993)

    MATH  Google Scholar 

  9. Dade, E.C.: Normal subgroups of M-groups need not be M-groups. Math. Zeit. 133, 313–317 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dornhoff, L.: M-groups and 2-groups. Math. Zeit. 100, 226–256 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  11. Feit, W., Seitz, G.M.: On finite rational groups and related topics. Ill. J. Math 33(1), 103–131 (1988)

    MathSciNet  MATH  Google Scholar 

  12. How, G. A.: Some classes of monomial groups. PhD thesis, Australian National University (1980)

  13. Isaacs, I.M.: Character theory of finite groups. Dover, Mineola (1994)

    MATH  Google Scholar 

  14. Isaacs, I.M.: Characters of Solvable Groups. Graduate Studies in Mathematics, vol. 189. American Mathematical Society, Providence (2018)

    MATH  Google Scholar 

  15. James, G., Kerber, A.: The Representation Theory of the Symmetric Group. Addison-Wesley, Boston (1991)

    Google Scholar 

  16. König, J.: Solvability of generalized monomial groups. J. Group Theory 13, 207–220 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nicolae, F.: On holomorphic Artin L-functions. Monatsh. Math. 186(4), 679–683 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  18. Springer, T.A.: A construction of representations of Weyl groups. Invent. Math. 44(3), 279–293 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  19. Taketa, K.: Über die Gruppen, deren Darstellungen sich sämtlich auf monomiale Gestalt transformieren lassen. Proc. Acad. Tokyo 6, 31–33 (1930)

    MathSciNet  MATH  Google Scholar 

  20. The GAP Group: GAP Groups, Algorithms, and Programming, Version 4.10.2. https://www.gap-system.org (2019)

  21. van der Waall, R.W.: On the embedding of minimal non-M-groups. Indag. Math. 77, 157–167 (1974)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS - UEFISCDI, project number PN-III-P1-1.1-TE-2021-1633, within PNCDI III.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mircea Cimpoeaş.

Ethics declarations

Conflict of interest

The author has no relevant financial or non-financial interests to disclose.

Additional information

Communicated by John S. Wilson.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cimpoeaş, M. On a generalization of monomial groups. Monatsh Math 202, 53–64 (2023). https://doi.org/10.1007/s00605-022-01762-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-022-01762-6

Keywords

Mathematics Subject Classification

Navigation