The Frattini subgroups of subgroups of hyperbolic groups
Copyright policy )The Frattini subgroups of subgroups of hyperbolic groups
The article under review is dedicated to the Frattini subgroup of a finitely generated word-hyperbolic group. The author proves that the Frattini subgroup of any finitely generated subgroup of a word-hyperbolic group is finite nilpotent (Theorem A), and the Frattini subgroup of a finitely generated residually torsion-free word-hyperbolic group is identity (Corollary B). He also obtains the finiteness of the near Frattini subgroup of any finitely generated subgroup of a word-hyperbolic group (Theorem C).
Hyperbolic groups and nonpositively curved groups, Topological methods in group theory, Frattini subgroup, Maximal subgroups, Subgroup theorems; subgroup growth, word-hyperbolic groups, maximal subgroups, finitely generated groups, Cayley graphs
Hyperbolic groups and nonpositively curved groups, Topological methods in group theory, Frattini subgroup, Maximal subgroups, Subgroup theorems; subgroup growth, word-hyperbolic groups, maximal subgroups, finitely generated groups, Cayley graphs
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