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Concerning automorphisms in finitely generated Abelian groups

Published online by Cambridge University Press:  24 October 2008

H. Liebeck
H. Liebeck
Affiliation:
Department of Mathematics, University of Keele, Staffordshire
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Extract

Of particular importance in the structure theory of finitely generated groups are those groups G having the property ℳd that for any two sets of generators g1, …, gd; h1, …, hd of G there is an automorphism θ of G such that (i = 1, …, d). Gaschütz(1) proved that all groups G having† ℳd also possess a further manifestation of symmetry, the property that if M and N are finite normal subgroups of G, any isomorphism between G/M and G/N can be induced by an automorphism of G. The case in which G is a finite p-group had previously been considered by Taunt (6) and Liebeck(2), who proved that for such groups the above property on the quotient groups of G is equivalent to ℳd.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 25 - 31
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

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