2015/03/20 by Olga Kulikova, Kulikova, Olga
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1503.06195
13 pages
arxiv created 2015/03/20 · arxiv updated 2015/03/23
Consider a presentation P=<\bf x|\bf \bigcupi=1n ri>. Let \bf Ri be the normal closure of the set \bf ri in the free group \bf F with basis \bf x, Pi=<\bf x|\bf ri>, \bf Ni = ∏j≠ i\bf Rj. In the present article, using geometric techniques of pictures, generators for \frac\bf Ri∩ \bf Ni[\bf Ri, \bf Ni], i=1,...,n, are obtained from a set of generators over \Pi| i=1,..., n\ for π2(P). As a corollary, we get a sufficient condition for the family \\bf R1,...,\bf Rn\ to be independent.