Abstract
We show that every solvable group is a subgroup of some monomial real group. This extends a result of Dade, who proved that every solvable group is a subgroup of a monomial group.
Similar content being viewed by others
References
Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of Finite Groups. Clarendon Press, Oxford (1985)
Feit, W., Seitz, G.: On finite rational groups and related topics. Illinois. J. Math. 33, 103–131 (1988)
Gow, R.: Groups whose characters are rational-valued. J. Algebra 40, 280–299 (1976)
Huppert, B.: Endliche Gruppen I. Spinger, Berlin (1967)
Isaacs, M.: Character Theory of Finite Groups. Dover Publications Inc, New York (1994)
Mattarei, S.: On character tables of wreath products. J. Algebra 175(1), 157–178 (1995)
Tent, J.: Quadratic rational solvable groups. J. Algebra 363, 73–82 (2012)
Thompson, J.: Composition factors of rational finite groups. J. Algebra 319, 558–594 (2008)
Tiep, P.H., Zalesski, A.: Real conjugacy classes in algebraic groups and finite groups of Lie type. J. Group Theory 8, 291–315 (2005)
Trefethen, S.: Non-abelian composition factors of \(m\)-rational groups. J. Algebra 485, 288–309 (2017)
Acknowledgements
Research supported by Ministerio de Ciencia e Innovación PID-2019-103854GB-100, Generalitat Valenciana AICO/2020/298 and FEDER funds. We thank the referee for helpful comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Moretó, A., Tent, J.F. Solvable real groups. Arch. Math. 116, 481–485 (2021). https://doi.org/10.1007/s00013-020-01561-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-020-01561-1