On soluble groups whose subnormal subgroups are inert

Document Type : Ischia Group Theory 2014

Authors

1 Dipartimento Matematica e Appl., v. Cintia, M.S.Angelo 5a, I-80126 Napoli (Italy)

2 Dipartimento di Matematica, Informatica ed Economia, Universita della Basilicata, Viale dell'Ateneo Lucano 10, I-85100

Abstract

A subgroup H of a group G is called inert if‎, ‎for each $g\in G$‎, ‎the index of $H\cap H^g$ in $H$ is finite‎. ‎We give a classification of soluble-by-finite groups $G$ in which subnormal subgroups are inert in the cases where $G$ has no nontrivial torsion normal subgroups or $G$ is finitely generated‎.

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References

V. V. Belyaev, M. Kuzucuoglu and E. Seckin (1999). Totally inert groups. Rend. Sem. Mat. Univ. Padova. 102, 151-156 U. Dardano and S. Rinauro (2012). Inertial automorphisms of an abelian group. Rend. Semin. Mat. Univ. Padova. 127, 213-233 U. Dardano and S. Rinauro Inertial endomorphisms of an abelian group. Ann. Mat. Pura Appl., to app ear, ( DOI: 10.1007/s10231-014-0459-6 ). U. Dardano and S. Rinauro (2014). On the ring of inertial endomorphisms of an abelian group. Ric. Mat.. 63 (1), 103-115 U. Dardano and S. Rinauro The group of inertial automorphisms of an abelian group. (submitted), see also ( arXiv:1403.4193 ). M. De Falco, F. de Giovanni, C. Musella and N. Trabelsi (2013). Strongly Inertial Groups. Comm. Algebra. 41 (6), 2213-2227 M. R. Dixon, M. J. Evans and A. Tortora (2010). On totally inert simple groups. Cent. Eur. J. Math.. 8 (1), 22-25 F. de Giovanni (2013). Some Trends in the Theory of Groups with Restricted Conjugacy Classes. Note Mat.. 33 (1), 71-87 J. C. Lennox and D. J. S. Robinson (2004). The theory of infinite soluble groups. Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford. D. J. S. Robinson (1996). A Course in the Theory of Groups. second edition, Springer-Verlag, New York. 80 D. J. S. Robinson (2006). On inert subgroups of a group. Rend. Sem. Mat. Univ. Padova. 115, 137-159
International Journal of Group Theory
Volume 4, Issue 2 - Serial Number 2
Proceedings of the Ischia Group Theory 2014-Part II.
June 2015
Pages 17-24

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History

  • Receive Date: 13 March 2015
  • Revise Date: 05 May 2015
  • Accept Date: 06 May 2015
  • Published Online: 01 June 2015

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