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On groups of finite height

Published online by Cambridge University Press:  09 April 2009

Stephen J. Pride
Stephen J. Pride
Affiliation:
Faculty of Mathematics Open UniversityMilton Keynes MK7 6AA, England
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Abstract

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In a previous paper, ‘The concept of “largeness” in group theory’, a partial order was defined on the class of infinite groups, and this partial order was seen to give some precision to our intuitive notions of what it means for one infinite group to be ‘larger’ than another. The aim of this paper is to look more closely at groups which are ‘low down’ in this partial order, and to examine the interplay between properties of groups and finiteness conditions in group theory.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 E 15, 20 F 15, 20 K 10, 20 K 25; secondary 20 E 10.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 87 - 99
Copyright
Copyright © Australian Mathematical Society 1979

References

Baumslag, B. and Pride, S. J. (1978), ‘Groups with two more generators than relators’, J. London Math. Soc., (2) 17, 425–426.CrossRefGoogle Scholar
Hales, A. (1979), ‘Groups of height four’, preprintGoogle Scholar
Neumann, B. H. and Yamamuro, S. (1965), ‘Boolean powers of simple groups’ J. Austral. Math. Soc. 5, 315–324.CrossRefGoogle Scholar
Neumann, H. (1967), Varieties of groups (Ergebnisse der Mathematik, Bd 37, Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Pride, S. J. (to appear) ‘The concept of “largeness” in group theory’, Proc. Conf. on Word and Decision Problems in Algebra and Group Theory (Oxford).Google Scholar
Robinson, D. J. S. (1972), Finiteness conditions and generalized soluble groups Vol. I (Ergebnisse der Mathematik, Bd 62, Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Rotman, J. J. (1973), The theory of groups: an introduction (2nd edition, Allyn and Bacon, Boston).Google Scholar
Scott, W. R. (1964), Group theory (Prentice-Hall, Englewood Cliffs, New Jersey).Google Scholar
Tretkoff, C. (1976), ‘Some remarks on just-infinite groups’, Comm. Algebra 4, 483–489.CrossRefGoogle Scholar
Wilson, J. S. (1970), ‘Groups satisfying the maximal condition for normal subgroups’, Math. Z. 118, 107–114.CrossRefGoogle Scholar
Wilson, J. S. (1971), ‘Groups with every proper quotient finite’, Proc. Camb. Phil. Soc. 69, 373–391.CrossRefGoogle Scholar
Wolf, J. A. (1968), ‘Growth of finitely generated solvable groups and curvature of Riemannian manifolds’, J. Differential Geometry 2, 421–446.CrossRefGoogle Scholar