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On the Frattini subgroup of the generalized free product with amalgamation

Authors: D. Ž. Djoković and C. Y. Tang
Journal: Proc. Amer. Math. Soc. 32 (1972), 21-23
MSC: Primary 20.54
MathSciNet review: 0289656
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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.

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  • [1] G. Higman and B. H. Neumann, On two questions of Itô, J. London Math. Soc. 29 (1954), 84-88. MR 15, 286. MR 0057881 (15:286g)
  • [2] A. Whittemore, On the Frattini subgroup, Trans. Amer. Math. Soc. 141 (1969), 323-333. MR 39 #6993. MR 0245687 (39:6993)

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Keywords: Group, Frattini subgroup, generalized free product with amalgamation, minimal condition
Article copyright: © Copyright 1972 American Mathematical Society

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