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Edjvet, M.
and
Pride, Stephen J.
1984.
Groups — Korea 1983.
Vol. 1098,
Issue. ,
p.
29.
Article contents
Groups of height four
Published online by Cambridge University Press: 09 April 2009
Abstract
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If G and H are infinite groups then G is said to be larger than H (H≼G) if there are subgroups A of G, B of H, each of finite index, such that B is an epimorphic image of A. Pride (1979) showed that if G has finite ‘height’ with respect to the quasi-order ≼ then there are only finitely many (classes of) minimal groups H with H ≼G, and asked whether this were true without the minimality restriction on H. This paper gives a negative answer to his question by exhibiting a group G of height four with infinitely many (classes of) groups H satisfying H≼G.
1980 Mathematics subject classification (Amer. Math. Soc.): 20 E 99, 20 K 15.
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- Research Article
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- Copyright © Australian Mathematical Society 1980
References
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