The computational complexity of the word problem in HNN-extension groups is studied. a fundamental construction combinatorial group theory. It shown that for an ascending H logspace reducible to so-called compressed H. main result paper states hyperbolic with cyclic associated subgroups can be solved polynomial time. This easily extended graphs vertex and edge groups.

We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, sense it has finite image abstract subgroup. Using this criterion we exhibit groups are CAT(0) but not biautomatic. These also resolve number other questions concerning groups.

Abstract In this paper we introduce the notion of existentially closed Leibniz algebras. Then use HNN-extensions algebras in order to prove an embedding theorem.

Abstract Recently, I. J. Leary and A. Minasyan [Commensurating HNN extensions: Nonpositive curvature biautomaticity, Geom. Topol. 25 (2021), 4, 1819–1860] studied the class of groups G ⁢ ( A , L stretchy="false">) </m:math...