A subgroup H of a group G is called commensurable with a normal subgroup (cn) if there is N C G such that |HN/(H ∩ N)| is finite. We characterize generalized radical groups G which have one of the following finiteness conditions: (A) the minimal condition on non-cn subgroups of G; (B) the non-cn subgroups of G fall into finitely many conjugacy classes; (C) the non-cn subgroups of G have finite rank
Groups with many subgroups which are commensurable with some normal subgroup / Dardano, U.; Rinauro, S.. - In: ADVANCES IN GROUP THEORY AND APPLICATIONS. - ISSN 2499-1287. - 7:(2019), pp. 3-13. [10.32037/agta-2019-002]
Groups with many subgroups which are commensurable with some normal subgroup
Dardano U.
;
2019
Abstract
A subgroup H of a group G is called commensurable with a normal subgroup (cn) if there is N C G such that |HN/(H ∩ N)| is finite. We characterize generalized radical groups G which have one of the following finiteness conditions: (A) the minimal condition on non-cn subgroups of G; (B) the non-cn subgroups of G fall into finitely many conjugacy classes; (C) the non-cn subgroups of G have finite rankFile in questo prodotto:
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