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Groups of height four

Published online by Cambridge University Press:  09 April 2009

Alfred W. Hales
Alfred W. Hales
Affiliation:
Department of Mathematics University of California, Los Angeles, U.S.A.
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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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 297 - 300
Copyright
Copyright © Australian Mathematical Society 1980

References

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