TY - JOUR

T1 - On the intersection of finitely generated subgroups in free products of groups

AU - Ivanov, Sergei V

PY - 1999

Y1 - 1999

N2 - A subgroup H of a free product Π*αεI Gα of groups Gα, α ε I, is called factor free if for every S ε Π*αεI Gα and β ε I one has SHS-1 ∩ Gβ = {1} (by Kurosh theorem on subgroups of free products, factor free subgroups are free). If K is a finitely generated free group, denote γγ̄(K) = max(γ(K) -1,0), where γ(K) is the rank of K. It is proven that if H, K are finitely generated factor free subgroups of a free product Π*αεI Gα then γ̄(H∩K) ≤ 6γ̄(H)γ̄(K). It is also shown that the inequality γ̄(H∩K) ≤ γ̄(H)γ̄(K) of Hanna Neumann conjecture on subgroups of free groups does not hold for factor free subgroups of free products.

AB - A subgroup H of a free product Π*αεI Gα of groups Gα, α ε I, is called factor free if for every S ε Π*αεI Gα and β ε I one has SHS-1 ∩ Gβ = {1} (by Kurosh theorem on subgroups of free products, factor free subgroups are free). If K is a finitely generated free group, denote γγ̄(K) = max(γ(K) -1,0), where γ(K) is the rank of K. It is proven that if H, K are finitely generated factor free subgroups of a free product Π*αεI Gα then γ̄(H∩K) ≤ 6γ̄(H)γ̄(K). It is also shown that the inequality γ̄(H∩K) ≤ γ̄(H)γ̄(K) of Hanna Neumann conjecture on subgroups of free groups does not hold for factor free subgroups of free products.

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U2 - 10.1142/S021819679900031X

DO - 10.1142/S021819679900031X

M3 - Article

AN - SCOPUS:0346786574

SN - 0218-1967

VL - 9

SP - 521

EP - 528

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 5

ER -