Near Frattini subgroups of residually finite generalized free products of groups | Zendy

Mohammad K. Azarian | Zendy

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Near Frattini subgroups of residually finite generalized free products of groups

Author(s) -

Mohammad K. Azarian

Publication year - 2001

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/s0161171201005397

Subject(s) - mathematics , combinatorics , free product , finitely generated abelian group , nilpotent , product (mathematics) , group (periodic table) , geometry , chemistry , organic chemistry

Let G=A★HB be the generalized free product of the groups A and B with the amalgamated subgroup H. Also, let λ(G) and ψ(G) represent the lower near Frattini subgroup and the near Frattini subgroup of G, respectively. If G is finitely generated and residually finite, then we show that ψ(G)≤H, provided H satisfies a nontrivial identical relation. Also, we prove that if G is residually finite, then λ(G)≤H, provided: (i) H satisfies a nontrivial identical relation and A,B possess proper subgroups A1,B1 of finite index containing H; (ii) neither A nor B lies in the variety generated by H; (iii) H

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