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GROUPS WITH NORMALITY CONDITIONS FOR UNCOUNTABLE SUBGROUPS

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  18 March 2020

M. DE FALCO ,
F. DE GIOVANNI  and
C. MUSELLA
M. DE FALCO
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli, Italy e-mail: mdefalco@unina.it
F. DE GIOVANNI
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli, Italy e-mail: degiovan@unina.it
C. MUSELLA
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli, Italy e-mail: cmusella@unina.it
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Abstract

This paper continues the investigation of the structure of uncountable groups whose large subgroups are normal. Moreover, we describe the behaviour of uncountable groups in which every large subgroup is close to normal with the only obstruction of a finite section.

Keywords

uncountable groupnormal subgroup

MSC classification

Primary: 20F24: FC-groups and their generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 111 , Issue 2 , October 2021 , pp. 268 - 277
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by B. Martin

Dedicated to Leonid A. Kurdachenko on the occasion of his 70th birthday

References

De Falco, M., de Giovanni, F., Heineken, H. and Musella, C., ‘Normality in uncountable groups’, Adv. Group Theory Appl. 3 (2017), 13–29.Google Scholar
De Falco, M., de Giovanni, F. and Musella, C., ‘Groups with normality conditions for subgroups of infinite rank’, Publ Mat. 58 (2014), 331–340.Google Scholar
De Falco, M., de Giovanni, F., Musella, C. and Sysak, Y. P., ‘Uncountable groups in which normality is a transitive relation’, Internat. J. Algebra Comput. 29 (2019), 627–638.Google Scholar
De Falco, M., Evans, M. J., de Giovanni, F. and Musella, C., ‘Permutability in uncountable groups’, Ann. Mat. Pura Appl. 197 (2018), 1417–1427.Google Scholar
de Giovanni, F. and Trombetti, M., ‘Uncountable groups with restrictions on subgroups of large cardinality’, J. Algebra 447 (2016), 383–396.Google Scholar
Ehrenfeucht, A. and Faber, V., ‘Do infinite nilpotent groups always have equipotent abelian subgroups?’, Kon. Nederl. Akad. Wet. A 75 (1972), 202–209.Google Scholar
Fedorov, Y. G., ‘On infinite groups every non-trivial subgroup of which has finite index’, Uspekhi Mat. Nauk 6 (1951), 187–189.Google Scholar
Franciosi, S. and de Giovanni, F., ‘Groups satisfying the minimal condition on certain non-normal subgroups’, in: Groups—Korea ’94 (de Gruyter, Berlin), 107–118.Google Scholar
Kurdachenko, L. A., Levishchenko, S. S. and Semko, N. N., ‘Groups with almost normal infinite subgroups’, Soviet Math. (Izv. VUZ) 27 (1983), 73–81.Google Scholar
Lennox, J. C. and Robinson, D. J. S., The Theory of Infinite Soluble Groups (Clarendon Press, Oxford, 2004).Google Scholar
Neumann, B. H., ‘Groups with finite classes of conjugate subgroups’, Math. Z. 63 (1955), 76–96.Google Scholar
Obraztsov, V. N., ‘An embedding theorem for groups and its corollaries’, Math. USSR-Sb. 66 (1990), 541–553.Google Scholar
Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups (Springer, Berlin, 1972).Google Scholar
Semenova, T. J., ‘On nilpotent subgroups of FC-groups’, in: Some Problems in the Theory of Groups and Rings (Inst. Fiz. im. Kirenskogo Sibirsk. Otdel. Akad. Nauk SSSR, Krasnoyarsk, 1973), 150–159.Google Scholar
Shelah, S., ‘On a problem of Kurosh, Jónsson groups and applications’, in: Word Problems II—the Oxford Book (North-Holland, Amsterdam, 1980), 373–394.Google Scholar
Tomkinson, M. J., FC-groups (Pitman, Boston, 1984).Google Scholar
Wilson, J. S., ‘Some properties of groups inherited by normal subgroups of finite index’, Math. Z. 114 (1970), 19–21.Google Scholar