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On the Frattini Subgroups of Generalized Free Products with Cyclic Amalgamations(1)

Published online by Cambridge University Press:  20 November 2018

C. Y. Tang
C. Y. Tang*
Affiliation:
University of Waterloo, Waterloo, Ontario
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In [1] Higman and Neumann asked the questions whether the Frattini subgroup of a generalized free product can be larger than the amalgamated subgroup and whether such groups necessarily have maximal subgroups. In [4] Whittemore gave answers to the special cases of generalized free products of finitely many free groups with cyclic amalgamation and of generalized free products of finitely many finitely generated abelian groups. In this paper we shall study the Frattini subgroups of generalized free products of any groups with cyclic amalgamation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 569 - 573
Copyright
Copyright © Canadian Mathematical Society 1972

Footnotes

(1)

This work was partly supported by National Research Council Grant A-4064.

References

1. Higman, G. and Neumann, B. H., On two questions of Itô, J. London. Math. Soc. 29 (1954), 84-88.Google Scholar
2. Neumann, B. H., An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London Ser. A, 246(1954), 503-554.Google Scholar
3. Scott, W. R., Group theory, Prentice-Hall, Englewood Cliffs, N.J., 1964.Google Scholar
4. Whittemore, A., On the Frattini subgroups, Trans. Amer. Math. Soc. (406) 141(1969), 323-334.Google Scholar