Fundamental group of asymptotic cones of abelian-by-cyclic groups. (Q2255148)

The paper generalizes a result of \textit{J. Burillo} [J. Lond. Math. Soc., II. Ser. 59, No. 2, 557-572 (1999; Zbl 0922.20047)]. The main theorem states that the fundamental group of the asymptotic cone of an abelian-by-cyclic group contains the Hawaiian Earring group, thus is uncountable and nonfree. The author constructs a subspace of such asymptotic cone, which is homotopy equivalent to the Hawaiian Earring.