Infinitely many not locally soluble $SI^*$-groups

Details Infinitely many not locally soluble $SI^*$-groups Infinitely many not locally soluble $SI^*$-groups

2012-01-25

arxiv.org/abs/1201.5322v1

Ricerche di Matematica, 52 (2003), 1--19

Mathematics

Group Theory

16 pages

Scientific paper

The class of those (torsion-free) $SI^*$-groups which are not locally soluble, has the cardinality of the continuum. Moreover, these groups are not only pairwise non-isomorphic, but also they generate pairwise different varieties of groups. Thus, the set of varieties generated by not locally soluble $SI^*$-groups is of the same cardinality as the set of all varieties of groups. It is possible to localize a variety of groups which contains all groups and varieties constructed. The examples constructed here continue the well known example of a not locally soluble $SI^*$-group built by Hall and by Kov\'acs and Neumann.

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