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Intersections of conjugates of Magnus subgroups of
one-relator groups
Donald J Collins
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Geometry & Topology Monographs 14
(2008) 135–171
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Abstract
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In the theory of one-relator groups, Magnus subgroups, which are free subgroups obtained by omitting a generator that occurs in the given relator, play an essential structural role. In a previous article, the author proved that if two distinct Magnus subgroups M and N of a one-relator group, with free bases S and T are given, then the intersection of M and N is either the free subgroup P generated by the intersection of S and T or the free product of P with an infinite cyclic group.
The main result of this article is that if M and N are Magnus subgroups (not necessarily distinct) of a one-relator group G and g and h are elements of G, then either the intersection of gMg-1 and hNh-1 is cyclic (and possibly trivial), or gh-1 is an element of NM in which case the intersection is a conjugate of the intersection of M and N.
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Keywords
one-relator group, Magnus subgroup
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Mathematical Subject Classification
Primary: 20F05
Secondary:
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Publication
Received: 14 March 2006
Accepted: 30 January 2007
Published: 29 April 2008
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