Chain Conditions for Subgroups of Infinite Order or Index
Paek, Dae Hyun
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https://hdl.handle.net/2142/86979
Description
Title
Chain Conditions for Subgroups of Infinite Order or Index
Author(s)
Paek, Dae Hyun
Issue Date
1999
Doctoral Committee Chair(s)
Derek J.S.Robinson
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
Groups with max-infinityi or min-infinityi for i=empty,s,n are the subject of this dissertation. Abelian, nilpotent, and solvable groups with max-infinity or min-infinity are examined in detail and structure theorems are given in each case. We then characterize the groups with max-infinity or min-infinity in the smallest class of groups containing all linear groups which is locally closed and closed with respect to the formation of ascending series with factors in the class. In addition, we discuss characterizations of solvable groups and subsolvable groups with max-infinitys or min-infinitys. Investigations of locally nilpotent and metanilpotent groups with max-infinityn or min-infinity n are included as final topics.
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