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On the range of finite embeddings of a finite amalgam

Published online by Cambridge University Press:  18 May 2009

Abdul Majeed
Abdul Majeed
Affiliation:
University of the Punjab, Lahore, Pakistan
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Certain questions about the range of finite embeddings of a finite amalgam were discussed in [3]. Another pertinent question is the following.

If a finite reduced amalgam has both an infinite and a finite embedding, does it have a maximal finite embedding such that all other finite embeddings are its homomorphic images? We give a counter example to answer this question in the negative. The finite amalgam considered will involve a group from the family of groups of the type (l, m; n, k) discussed by Coxeter [2] having the following presentation

These groups may be regarded as factor groups of

which is known to be finite if

and infinite otherwise.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 142 - 143
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Burnside, W., Theory of groups of finite order (Cambridge, 1911).Google Scholar
2.Coxeter, H. S. M., The abstract groups Gm,n,p, Trans Amer. Math. Soc. 45 (1939), 73–150.Google Scholar
3.Majeed, A., On embeddable finite amalgams of groups, Glasgow Math. J. 13 (1972), 135–141.CrossRefGoogle Scholar