On the residual properties of Baumslag–Solitar groups

Abstract

A survey of results on the residual properties of Baumslag -Solitar groups which have been obtained to date.

On finite state automaton actions of HNN extensions of free abelian groups

“…Consider each part of equality (3). Split out an infinite word w on the blocks of the length n (see (2)).…”

“…As an interesting corollary we obtain that corresponding HNN extensions are residually p-finite. For our best knowledge residually p-finite ascending HNN extension of free abelian groups are described only for the case n = 1 (see [3] and references therein). Isomorphic embeddings of these groups into p-FGA(X) were constructed in [1].…”

Baumslag-Solitar groups and residual nilpotence

“…Our work is concerned with the residual nilpotence of these groups. A survey about the residual properties of these groups is given in [11]. In [1], Bardakov and Neschadim studied the lower central series of Baumslag-Solitar groups and computed the intersection of all terms of the lower central series for some special cases of the non-residually nilpotent Baumslag-Solitar groups.…”

On the lower central series of some virtual knot groups

“…Necessary and sufficient conditions for p-residual finiteness of BS(m, n) were found by D. I. Moldavanskii [7] (see also [10]). PROPOSITION B ( [7,10]).…”

“…Necessary and sufficient conditions for p-residual finiteness of BS(m, n) were found by D. I. Moldavanskii [7] (see also [10]). PROPOSITION B ( [7,10]). BS(m, n) is p-residually finite if and only if m = 1 and n ≡ 1 (mod p), or n = m = p r for some r ≥ 0, or n = −m for m = 2 r , r ≥ 0.…”