Let G he the direct sum of n ≥ 2 copies of the cyclic group, Z , of integers. Let p be a fixed prime and α ≥ 1 a fixed integer. Consider the subgroups, λ , of G of index p[superscript]α in G .
Let S be a subset of G. We say S is a stellar set if ax ε S implies
(1.1) x,2x,...,ax ε S for any x ε G and any integer
a ≥ 1 .
Suppose S is a stellar set, p[superscript]α G ∩ S = ∅, and S intersects all the subgroups λ of G of index p[superscript]α in G . We shall show that then
|S| ≥ p[superscript]α + P[superscript]α-1. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/35550 |
| Date | January 1969 |
| Creators | Harris, L. F. |
| 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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