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Modular and dual-Dedekind subgroups in certain classes of infinite groups
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Segal, Judith Ann (1975) Modular and dual-Dedekind subgroups in certain classes of infinite groups. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1747669~S15
Abstract
The main inspiration of this thesis were the two papers of Schmidt ([I] & [II]) and the paper of Menegazzo ([III]).
Chapter One is concerned with establishing some basic results concerning modular subgroups, and Chapter Two with defining a class of groups * ( which includes the class of locally finite groups) and extending the theorems in Schmidt ([I]) to groups in this class. Chapter Three, which was the first chapter of the thesis to be written, examines the structure of modular subgroups in locally finite groups with the minimum condition on subgroups (where there is a definitive structure theorem to help us). Chapter Four extends the results of Schmidt ([II]) to locally finite groups. Finally, Chapter Five takes a (by no means exhaustive) look at dual-dedekind subgroups (i.e. subgroups which are dual to modular subgroups). A few theorems in the first section of Chapter Five are simply the dual of theorems in Chapter One; for the sake of clarity, however, their proofs are included.
After the main body of this thesis had been completed, my supervisor, Dr. S.E.Stonehewer, produced a definitive theorem concerning the structure of corefree modular subgroups in locally finite groups analogous to the main theorem of Schmidt ([II]). For the sake of completeness, this theorem is included in an appendix.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Modular groups, Infinite groups | ||||
| Official Date: | October 1975 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Stonehewer, S. E. | ||||
| Extent: | 81 leaves : illustrations, charts | ||||
| Language: | eng |
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