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- Title
On the Intersection of Finitely Generated Subgroups in Free Products of Groups.
- Authors
Ivanov, S. V.; Kharlampovich, O.
- Abstract
A subgroup H of a free product п*[SUBα∈I] G[SUBα] of groups G[SUBα], α ∈ I, is called factor free if for every S ∈ п*[SUBα∈I] G[SUBα] and β ∈ I one has SHS[SUP-1] ∩ G[SUBβ] = {1} ( by Kurosh theorem on subgroups of free products, factor free subgroups are free). IF K is a finitely generated free group, denote &rbar;(K) = max(r(K) - 1, 0), where r(K) is the rank of K. It is proven that if H, K are finitely generated factor free subgroups of a free product п*[SUBα∈I] G[SUBα] then &rbar; (H ∩ K) ≤ 6&rbar;(H)&rbar;(K). It is also shown that the inequality &rbar;(H∩&K) ≤&rbar;(H)&rbar;(K) of Hanna Neumann conjecture on subgroups of free groups does not hold for factor free subgroups of free products.
- Subjects
GROUP theory; FREE products (Group theory); FREE groups; LOGICAL prediction
- Publication
International Journal of Algebra & Computation, 1999, Vol 9, Issue 5, p521
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S021819679900031X