Abstract
Given a group G and subgroups X ⊞ Y , with Y of finite index in X , then in general it is not possible to determine the index | X : Y | simply from the lattice of subgroups of G . For example, this is the case when G has prime order. The purpose of this work is twofold. First we show that in any group, if the indices | X : Y | are determined for all cyclic subgroups X , then they are determined for all subgroups X . Second we show that if G is a group with an ascending normal series with factors locally finite or abelian, and if the Hirsch length of G is at least 3, then all indices | X : Y | are determined.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
