Subnormal subgroups in $U(\textbf {Z}G)$
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- by Jairo Gonçalves, Jürgen Ritter and Sudarshan Sehgal PDF
- Proc. Amer. Math. Soc. 103 (1988), 375-382 Request permission
Abstract:
Let $U$ be the unit group of the integral group ring of a finite group $G$. We prove that every subgroup of $U$ containing $G$ and almost subnormal in $U$ contains a noncyclic free group unless $G$ is abelian or a Hamiltonian $2$-group.References
- Anthony Bak, Subgroups of the general linear group normalized by relative elementary groups, Algebraic $K$-theory, Part II (Oberwolfach, 1980) Lecture Notes in Math., vol. 967, Springer, Berlin-New York, 1982, pp. 1–22. MR 689387
- Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
- 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. Hartley and P. F. Pickel, Free subgroups in the unit groups of integral group rings, Canadian J. Math. 32 (1980), no. 6, 1342–1352. MR 604689, DOI 10.4153/CJM-1980-104-3
- 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 A. G. Kurosh, The theory of groups. II, Chelsea, New York, 1956.
- Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283
- W. R. Scott, Group theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0167513
- Jean-Pierre Serre, Le problème des groupes de congruence pour SL2, Ann. of Math. (2) 92 (1970), 489–527 (French). MR 272790, DOI 10.2307/1970630
- Sudarshan K. Sehgal, Topics in group rings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 50, Marcel Dekker, Inc., New York, 1978. MR 508515
- J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972), 250–270. MR 286898, DOI 10.1016/0021-8693(72)90058-0
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 375-382
- MSC: Primary 20C05; Secondary 16A26
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943049-7
- MathSciNet review: 943049