On locally indicable groups

Nonpositive immersions, sectional curvature, and subgroup properties

“…The best known classes of locally indicable groups are torsion-free one-relator groups [4,5] and fundamental groups of irreducible 3-manifolds with boundary [14]. The following plays a role in the proof of Theorem 1.2.…”

Question de Whitehead et modules précroisés

“…Mais sa démonstration ne nécessite pas ces restrictions. Ce résultat a été généralisé depuis par Howie [22].…”

An algorithm for stem products and one-relator groups

“…From the results in [5], G is locally indicable and there is an epimorphism <f> : G -*• Z with kernel H. Since the centre of G is non-trivial, it is therefore not contained in H, but is contained in both A and B (see [1]). More specifically, the centre of G is infinite cyclic, generated by some power of a which is equal to some power of p. So we have that <f>(A) = pZ and $(B) = qZ for some p,qeZ with (p, q) = 1 and A = A" x (y) and B = B° x (5), 0(y) = P, <K<5) = 1 with <f>(a) = kp and </>(J?)…”

“…x*+i])-Hence, there is a unique epimorhism (p:G-»Z (modulo Aut(Z)) given by the mapping x, -> ^^ and x n+! -v b^&, where g -gcd(p t ... p n , q { ... q n ), such that the kernel H of 4> is free of finite rank (see also [5,9,10]). Using the presentation that is given for G we can easily calculate the image of each x, in Z by solving the system of equations p,<x, = q,a 1+ , with i = 1 , .…”