Chain Conditions for Subgroups of Infinite Order or Index

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Paek, Dae Hyun

Contributors dc:contributor

• Derek J.S.Robinson

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9944958

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86979