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The subgroup lattice index problem
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Stonehewer, Stewart E. and Zacher, Giovanni (2009) The subgroup lattice index problem. Journal of Group Theory, Vol.12 (No.6). pp. 859-872. doi:10.1515/JGT.2009.018 ISSN 1433-5883.
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Official URL: http://dx.doi.org/10.1515/JGT.2009.018
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 l(G) 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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Group Theory | ||||
Publisher: | Walter de Gruyter & Co | ||||
ISSN: | 1433-5883 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.12 | ||||
Number: | No.6 | ||||
Number of Pages: | 14 | ||||
Page Range: | pp. 859-872 | ||||
DOI: | 10.1515/JGT.2009.018 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | GNSAGA |
Data sourced from Thomson Reuters' Web of Knowledge
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