On the Frattini subgroup of the generalized free product with amalgamation

Djoković, D. Ž.; Tang, C. Y.

doi:10.1090/S0002-9939-1972-0289656-7

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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On the Frattini subgroup of the generalized free product with amalgamation
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by D. Ž. Djoković and C. Y. Tang PDF

Proc. Amer. Math. Soc. 32 (1972), 21-23 Request permission

Abstract:

Let G be the generalized free product of two groups A and B amalgamating their subgroup H. If H satisfies the minimal condition on subgroups then the Frattini subgroup of G is contained in H. When H is finite then this Frattini subgroup can be precisely determined.

References

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Alice Whittemore, On the Frattini subgroup, Trans. Amer. Math. Soc. 141 (1969), 323–333. MR 245687, DOI 10.1090/S0002-9947-1969-0245687-9