On intersections of normal subgroups in free groups
Let N₁ (respectively N₂) be a normal closure of a set R₁ = {ui} (respectively R₂ = {vj}) of cyclically reduced words of the free group F(A). In the paper we consider geometric conditions on R₁ and R₂ for N₁ ∩ N₂ = [N₁, N₂]. In particular, it turns out that if a presentation < A | R₁, R₂ >...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2003 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2003
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154676 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On intersections of normal subgroups in free groups / O.V. Kulikova // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 36–67. — Бібліогр.: 4 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Let N₁ (respectively N₂) be a normal closure
of a set R₁ = {ui} (respectively R₂ = {vj}) of cyclically reduced
words of the free group F(A). In the paper we consider geometric
conditions on R₁ and R₂ for N₁ ∩ N₂ = [N₁, N₂]. In particular, it
turns out that if a presentation < A | R₁, R₂ > is aspherical (for
example, it satisfies small cancellation conditions C(p)&T(q) with
1/p + 1/q = 1/2), then the equality N₁ ∩ N₂ = [N₁, N₂] holds.
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| ISSN: | 1726-3255 |