Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772116 | Journal of Algebra | 2017 | 17 Pages |
Abstract
Let G be a group. An element gâG is called a test element of G if for every endomorphism Ï:GâG, Ï(g)=g implies that Ï is an automorphism. Let F(X) be a free group on a finite non-empty set X, and let X=X1âX2ââ¦âXr be a finite partition of X into râ¥2 non-empty subsets. For i=1,2,â¦,r, let uiâãXiãâ¤F(X), and let w(z1,â¦,zr) be a word in the variables z1,â¦,zr. We give several sufficient conditions on ui (1â¤iâ¤r) and w for w(u1,â¦,ur) to be a test element of F(X). As an application of these results, we give examples of test elements of a free group of rank greater than two that are not test elements in any pro-p completion of the group.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ilir Snopce, Slobodan Tanushevski,