Central extensions of divisible groups |
Posted on:2012-08-26 | Degree:Ph.D | Type:Thesis |
University:University of Illinois at Urbana-Champaign | Candidate:Elliot, Jason Walter | Full Text:PDF |
GTID:2450390011956923 | Subject:Mathematics |
Abstract/Summary: | |
This thesis contributes to the classification of central extensions of divisible groups with finite abelian quotient, so called "d-ab extensions." We give a matrix classification of equivalence classes of d-ab extensions and explicitly provide a family of group presentations. We provide a criterion for determining when two d-ab extensions are isomorophic in the case when the quotient is homocyclic. When the kernel has rank 1, we parametrize isomorphism classes of d-ab extensions with homocyclic quotient by constructing a family of group presentations. We also give a general reduction of d-ab extensions to the case when the kernel and center of the extensions coincide. For this case we give a classification of isomorphism classes when the kernel has rank 1. We highlight the applications of central extensions of divisible groups to nilpotent groups. |
Keywords/Search Tags: | Extensions, Divisible, Kernel has rank |
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