LOG Groups and Cyclically Presented Groups

The cyclically presented groups with relators $x_ix_{i+k}x_{i+l}$

“…Using Theorem 2 of [14] and Theorem 3.2 of [10] we can obtain (the analogous result to Corollary 4.3) that the converse holds in many cases. For the interested reader we now state such a result where, for simplicity, we consider only the 'strongly irreducible' cases (see [14]).…”

“…(a generalization of Lemma 3.1 of [10]) gives that if à n .m; k/ is aspherical then Q n .m; k/ is aspherical. Using Theorem 2 of [14] and Theorem 3.2 of [10] we can obtain (the analogous result to Corollary 4.3) that the converse holds in many cases.…”

“…Theorem 4.1 of [3] gives necessary and sufficient conditions for R n .k; l/ to be aspherical. Following [1], [10], this approach was used in Theorem 4.3 of [6] to obtain sufficient conditions for P n .k; l/ to be aspherical. Unfortunately that theorem is incorrect, implying (for example) that P 9 .2; 3/ is an aspherical presentation whereas in fact it defines a metacyclic group of order 513.…”

Fibonacci Type Semigroups

“…Except for two groups, this was provided in [13], [17], [18], [10]. The unresolved groups are the Gilbert-Howie groups ( [13]) H(9, 4) = R (2,9,6,4) and H(9, 7) = R(2, 9, 3, 7). Theorem B therefore classifies the finite semigroups T (2, n, k, h) except for the two unresolved semigroups T (2, 9, 6, 4) and T (2, 9, 3, 7) (up to isomorphism and anti-isomorphism).…”

Asphericity of symmetric presentations

“…• The presentations P (2, n, 2, 1, t) define the groups H(n, t) studied in [16] and [10]. The group H(n, t) has infinite abelianization if and only if n ≡ 0 (mod 6) and t ≡ 2 (mod 6).…”