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oai:www.ideals.illinois.edu:2142/24095 2023-07-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Robinson, Derek J.S. Mineyev, Igor Robinson, Derek J.S. Ivanov, Sergei V. Ullom, Stephen V. Elliot, Jason W. 2011-05-25T14:59:49Z 2011-05-25T14:59:49Z 2011-05-25T14:59:49Z 2011-05 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-03-31T21:14:37Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Elliot_Jason.pdf: 505260 bytes, checksum: 9a714fcdbbbcc57092a5f8c973bee4d5 (MD5) Made available in DSpace on 2011-05-25T14:59:49Z (GMT). No. of bitstreams: 2 Elliot_Jason.pdf: 505260 bytes, checksum: 9a714fcdbbbcc57092a5f8c973bee4d5 (MD5) license.txt: 4062 bytes, checksum: 3a17ca82a6e2217410f8a0b7602909af (MD5) http://hdl.handle.net/2142/24095 en Copyright 2011 Jason Walter Elliot divisible groups central extensions nilpotent groups group extensions Central extensions of divisible groups Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD