On the Frattini subgroups of certain generalized free products of groups
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- by C. Y. Tang
- Proc. Amer. Math. Soc. 37 (1973), 63-68
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310073-6
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Abstract:
Let $G = (\prod \nolimits _{i \in I}^\ast {{A_i}{)_H}}$ be the generalized free product of the groups ${A_i}$ amalgamating the subgroup H. We show that if G is residually finite and the groups ${A_i}$ have compatible H-filters then the Frattini subgroup $\Phi (G)$ is contained in the maximal G-normal subgroup in H. If the groups ${A_i}$ are free and H is finitely generated of infinite index in one ${A_i}$ then $\Phi (G) = 1$. We also show that if H is simple then $\Phi (G) = 1$ or ${H^G}$.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 63-68
- MSC: Primary 20F25
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310073-6
- MathSciNet review: 0310073