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 } / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/34390 |
| Date | January 1971 |
| Creators | Hughes, Peter Walter |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| 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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