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- Embedding theorems in finite soluble groups
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Embedding theorems in finite soluble groups Hughes, Peter Walter
Abstract
By a group we will mean a finite soluble group. It is an interesting fact, (Pardoe [1]), that the subgroup closure of the class of groups P[symbol omitted], those with a unique complemented chief series, is all groups. Let X be the class of groups with a complemented chief series. We investigate the action of closure operations T such that TX = X upon P[symbol omitted]. The purpose of this is to find a collection of such closure operations whose join applied to P[symbol omitted] is X . In the course of this investigation we introduce a new closure operation M defined by; MY = { G | G = <X₁,•••,Xn>, X₁ ɛ Y, X₁ sn G, ( |G : X₁|,•••,|G : Xn| ) = 1 }
Item Metadata
Title |
Embedding theorems in finite soluble groups
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1971
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Description |
By a group we will mean a finite soluble group. It is an interesting fact, (Pardoe [1]), that the subgroup closure of the class of groups P[symbol omitted], those with a unique complemented chief series, is all groups. Let X be the class of groups with a complemented chief series. We investigate the action of closure operations T such that TX = X upon P[symbol omitted]. The purpose of this is to find a collection of such closure operations whose join applied to P[symbol omitted] is X . In the course of this investigation we introduce a new closure operation M defined by;
MY = { G | G = <X₁,•••,Xn>, X₁ ɛ Y,
X₁ sn G, ( |G : X₁|,•••,|G : Xn| ) = 1 }
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-05-10
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080468
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.