3 citations · 5 across the 12 of their papers we have counts for
16 papers · 1 filter
Unipotence of a double commutator with transvections
Ihechukwu Chinyere
Let be a nonzero commutative ring with identity, , and . We prove that there exist nonidentity transvections such that $\big[[σ,τ_1],…
Solvable groups defined by redundant cyclic presentations
Ihechukwu Chinyere
We study the two-generator one-relator groups defined by , and determine exactly which of them fail to contain a free subgroup…
Groups with special presentations and star-graph
Bridgette Amoako, Ihechukwu Chinyere, Bernard Bainson
We consider a question of Edjvet and Vdovina concerning which groups defined by special presentations are large. For each integer , we construct an -generator one-relat…
Proof of the Noferini-Williams conjecture for Gilbert-Howie groups
Ihechukwu Chinyere
The Gilbert-Howie groups form a notable subclass within the broader family of Fibonacci-type cyclically presented groups . Noferini and Williams conjectured that…
On the Classification of Perfect Prishchepov Groups
Layla Sorkatti, Ihechukwu Chinyere
The Prishchepov groups form a broad class of cyclically presented groups. We verify a conjectural characterisation of the perfect groups in this family. We first pro…
On the non-existence of finite groups with certain normal subgroups
Ihechukwu Chinyere
Problem 20.21 of Mazurov and Khukhro (Unsolved Problems in Group Theory: The Kourovka Notebook, 20th Issue, 2022), contributed by M.~Conder and attributed to G.~Verret, asks whethe…
All hyperbolic cyclically presented groups with positive length three relators
Ihechukwu Chinyere, Martin Edjvet, Gerald Williams
We consider the cyclically presented groups defined by cyclic presentations with generators whose relators are the positive length three relators $x_ix_{i+1}x_{i+m-…
Redundant relators in cyclic presentations of groups
Ihechukwu Chinyere, Gerald Williams
A cyclic presentation of a group is a presentation with an equal number of generators and relators that admits a particular cyclic symmetry. We characterise the orientable, non-ori…
Generalized polygons and star graphs of cyclic presentations of groups
Ihechukwu Chinyere, Gerald Williams
Groups defined by presentations for which the components of the corresponding star graph are the incidence graphs of generalized polygons are of interest as they are small cancella…
Fractional Fibonacci groups with an odd number of generators
Ihechukwu Chinyere, Gerald Williams
The Fibonacci groups are known to exhibit significantly different behaviour depending on the parity of . We extend known results for for odd to the family of F…
Perfect Prishchepov groups
Ihechukwu Chinyere, Bernard Oduoku Bainson
We study cyclically presented groups of type to determine when they are perfect. It turns out that to do so, it is enough to consider the Prishchepov groups, so modu…
Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups
Ihechukwu Chinyere, Gerald Williams
Building on previous results concerning hyperbolicity of groups of Fibonacci type, we give an almost complete classification of the (non-elementary) hyperbolic groups within this c…
Hyperbolicity of T(6) Cyclically Presented Groups
Ihechukwu Chinyere, Gerald Williams
We consider groups defined by cyclic presentations where the defining word has length three and the cyclic presentation satisfies the T(6) small cancellation condition. We classify…
Structure of words with short 2-length in a free product of groups
Ihechukwu Chinyere
Howie and Duncan observed that a word in a free product with length at least two and which is not a proper power can be decomposed as a product of two cyclic subwords each of which…
Non-triviality of some one-relator products of three groups
Ihechukwu Chinyere, James Howie
In this paper we study a group G which is the quotient of a free product of three non-trivial groups by the normal closure of a single element. In particular we show that if the re…
On One-relator products induced by generalised triangle groups
Ihechukwu Chinyere, James Howie
In this paper we study a group G which is the quotient of a free product of groups by the normal closure of a word that is contained in a in a subgroup which has the form of a gene…