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Factoring a group as an amalgamated free product

Published online by Cambridge University Press:  09 April 2009

Edward T. Ordman
Edward T. Ordman
Affiliation:
University of Kentucky Lexington, Kentucky, 40506, U.S.A.
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Even if in a decomposition of a group the Ai are completely indecomposable, there may be another decomposition with each Cj properly contained in some Ai a proper subgroup of B. The example of Bryce ([1], p. 636) may be modified, at the cost of having one Ai = B, so that I = J and Ci > Ai for all i. It is our object to study this relationship between decompositions of a group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 2 , March 1973 , pp. 222 - 227
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bryce, R. A., ‘A note on free products with normal amalgamation,’ J. Austral. Math. Soc. 8 (1968), 631–637.CrossRefGoogle Scholar
[2]Charles, S. Holmes, ‘Projectivities of free products,’ Rend. Sem. Math. Univ. Padova. 42 (1969), 341–387.Google Scholar
[3]Magnus, W., Karrass, A., Solitar, D., Combinatorial Group Theory (Interscience, New York, 1966).Google Scholar
[4]Ordman, E. T., ‘On subgroups of amalgamated free products,’ Proc. Cambridge Philos. Soc. 69 (1971), 13–23.CrossRefGoogle Scholar
[5]Stallings, J. R., ‘A topological proof of Grushko's theorem on free products’, Math. Z. 90 (1965), 1–8.CrossRefGoogle Scholar