Magnus intersections in one-relator products
نویسنده
چکیده
A recent result of D. J. Collins states that the intersection of two Magnus subgroups in a one-relator group consists either just of the ‘obvious’ intersection, or exceptionally of the free product of the obvious intersection with a free group of rank 1. In this paper, Collins’ result is generalised to apply to one-relator products of arbitrary locally-indicable groups. Moreover, a precise analysis is carried out of when ‘exceptional’ intersections can arise. In the classical case of a one-relator group, the problems of recognizing the existence of an exceptional intersection, and of finding a generator for it, are shown to be algorithmically soluble.
منابع مشابه
Intersections of conjugates of Magnus subgroups of one-relator groups
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 genera...
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