Groups with permutability conditions for subgroups of infinite rank

Document Type: Ischia Group Theory 2016

Authors

1 Dipartimento di Matematica e Fisica, Università degli Studi della Campania "Luigi Vanvitelli"

2 Dipartimento di Matematica e Applicazioni Renato Caccioppoli - Università degli Studi di Napoli Federico II

Abstract

In this paper, the structure of non-periodic generalized radical groups of infinite rank whose subgroups of infinite rank satisfy a suitable permutability condition is investigated.

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Main Subjects


[1] M. De Falco, F. de Giovanni and C. Musella, Groups with normality conditions for subgroups of infinite rank, Publ. Mat., 58 (2014) 331–340.

[2] M. De Falco, F. de Giovanni and C. Musella, Large soluble groups and the control of embedding properties, Ric. Mat., 63 (2014) 117–130.

[3] M. De Falco, F. de Giovanni, C. Musella and Y. P. Sysak, Groups in which every subgroup is nearly permutable, Forum Math., 15 (2003) 665–677.

[4] F. de Giovanni and C. Musella, Groups with nearly modular subgroup lattice, Colloq. Math., 88 (2001) 13–20.

[5] F. de Giovanni, C. Musella and Y. P. Sysak, Groups with almost modular subgroup lattice, J. Algebra, 243 (2001) 738–764.

[6] K. Iwasawa, On the structure of infinite M-groups, Japan J. Math., 18 (1943) 709–728.

[7] B. H. Neumann, Groups with finite classes of conjugate subgroups, Math. Z., 63 (1955) 76–96.

[8] O. Ore, Structures and group theory, I. Duke Math. J., 3 (1937) 149–173.

[9] D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Springer, Berlin, 1972.

[10] R. Schmidt, Subgroup lattices of groups, de Gruyter, Berlin, 1994.

[11] M. J. Tomkinson, FC-groups, Pitman, Boston, 1984.