Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-28T20:25:21.070Z Has data issue: false hasContentIssue false
  • English
  • Français

GROUPS OF INFINITE RANK WITH NORMALITY CONDITIONS ON SUBGROUPS WITH SMALL NORMAL CLOSURE

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  11 November 2015

ANNA VALENTINA DE LUCA  and
GIOVANNA DI GRAZIA
ANNA VALENTINA DE LUCA*
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I 80126 Napoli, Italy email [email protected]
GIOVANNA DI GRAZIA
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I 80126 Napoli, Italy email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Groups of infinite rank in which every subgroup is either normal or contranormal are characterised in terms of their subgroups of infinite rank.

Keywords

infinite rankcontranormal subgrouplocally graded group

MSC classification

Primary: 20E15: Chains and lattices of subgroups, subnormal subgroups
Secondary: 20F19: Generalizations of solvable and nilpotent groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 48 - 53
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

De Falco, M., de Giovanni, F. and Musella, C., ‘Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank’, Colloq. Math. 131 (2013), 233–239.Google Scholar
De Falco, M., de Giovanni, F. and Musella, C., ‘Groups whose proper subgroups of infinite rank have a transitive normality relation’, Mediterr. J. Math. 10 (2013), 1999–2006.Google Scholar
De Falco, M., de Giovanni, F., Musella, C. and Sysak, Y. P., ‘Groups of infinite rank in which normality is a transitive relation’, Glasg. Math. J. 56 (2014), 387–393.CrossRefGoogle Scholar
De Falco, M., de Giovanni, F., Musella, C. and Sysak, Y. P., ‘On metahamiltonian groups of infinite rank’, J. Algebra 407 (2014), 135–148.CrossRefGoogle Scholar
De Falco, M., de Giovanni, F., Musella, C. and Trabelsi, N., ‘Groups with restrictions on subgroups of infinite rank’, Rev. Mat. Iberoam. 30(2) (2014), 535–548.Google Scholar
De Falco, M., Kurdachenko, L. A. and Subbotin, I. Ya., ‘Groups with only abnormal and subnormal subgroups’, Atti Semin. Mat. Fis. Univ. Modena 46 (1998), 435–442.Google Scholar
Dixon, M. R., Evans, M. J. and Smith, H., ‘Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank’, J. Pure Appl. Algebra 135 (1999), 33–43.Google Scholar
Evans, M. J. and Kim, Y., ‘On groups in which every subgroup of infinite rank is subnormal of bounded defect’, Comm. Algebra 32 (2004), 2547–2557.Google Scholar
Kurdachenko, L. A. and Smith, H., ‘Groups in which all subgroups of infinite rank are subnormal’, Glasg. Math. J. 46 (2004), 83–89.CrossRefGoogle Scholar
Malcev, A. I., ‘On some classes of infinite soluble groups’, Mat. Sbornik N. S. 28 (1951), 567–588; Amer. Math. Soc. Transl. Ser. 2 (1956), 1–21.Google Scholar
Robinson, D. J. S., A Course in the Theory of Groups (Springer, New York, 1996).Google Scholar
Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Group (Springer, New York–Berlin, 1972).Google Scholar
Rose, J. S., ‘Finite soluble groups with pronormal system normalizers’, Proc. Lond. Math. Soc. (3) 17 (1967), 447–469.Google Scholar
Subbotin, I. Ya., ‘Groups with alternatively normal subgroups’, Russian Math. 36 (1992), 87–89.Google Scholar