Papers by Russell D Blyth
Canadian Journal of Mathematics, 1989
... 15. MJ Tomkinson, FC-groups, Research Notes in Mathematics 96 (Pitman, London, 1984). Saint L... more ... 15. MJ Tomkinson, FC-groups, Research Notes in Mathematics 96 (Pitman, London, 1984). Saint Louis University, St. ... Le tarif d'abonnement pour 1989 est de 250$; les membres de la SMC ont droit a un abonnement au tarif reduit de 125$. ...
Contemporary Mathematics, 2008
We determine the nonabelian tensor squares and related homological functors of the free nilpotent... more We determine the nonabelian tensor squares and related homological functors of the free nilpotent groups of finite rank.
We determine the nonabelian tensor squares and related homo-logical functors of the free nilpoten... more We determine the nonabelian tensor squares and related homo-logical functors of the free nilpotent groups of finite rank.
Aspects of Infinite Groups - A Festschrift in Honor of Anthony Gaglione, 2008
We provide a detailed structure description of the derived subgroups of the free nilpotent groups... more We provide a detailed structure description of the derived subgroups of the free nilpotent groups of finite rank. This description is then applied to computing the nonabelian tensor squares of the free nilpotent groups of finite rank.
Journal of Algebra, 2015
ABSTRACT A covering of a group is a finite set of proper subgroups whose union is the whole group... more ABSTRACT A covering of a group is a finite set of proper subgroups whose union is the whole group. A covering is minimal if there is no covering of smaller cardinality, and it is nilpotent if all its members are nilpotent subgroups. We complete a proof that every group that has a nilpotent minimal covering is solvable, starting from the previously known result that a minimal counterexample is an almost simple finite group.
ISCHIA GROUP THEORY 2010 - Proceedings of the Conference, 2012
We provide a method for computing the nonabelian tensor square for any polycyclic group. We provi... more We provide a method for computing the nonabelian tensor square for any polycyclic group. We provide an implementation of this method for finitely generated nilpotent groups and use it to compute the nonabelian tensor square of the free nilpotent of class 3 groups of rank n.
Proceedings of the Edinburgh Mathematical Society, 2004
In this paper we compute the nonabelian tensor square for the free 2-Engel group of rank n > 3. T... more In this paper we compute the nonabelian tensor square for the free 2-Engel group of rank n > 3. The nonabelian tensor square for this group is a direct product of a free abelian group and a nilpotent group of class 2 whose derived subgroup has exponent 3. We also compute the nonabelian tensor square for one of the group's finite homomorphic images, namely, the Burnside group of rank n and exponent 3.
Journal of Pure and Applied Algebra, 1991
Blyth, R.D. end D.
Journal of the London Mathematical Society, 1990
Journal of Algebra, 2009
In this paper we develop the theory of computing the nonabelian tensor squares of polycyclic grou... more In this paper we develop the theory of computing the nonabelian tensor squares of polycyclic groups. The nonabelian tensor square G⊗G of any group G is isomorphic to a subgroup K of the derived subgroup of a cover group ν(G). We develop a general commutator calculus in K that models computations in G ⊗ G. We show that if G is polycyclic, then the cover group ν(G) is also polycyclic, and we give a finite presentation for ν(G) based on a presentation for G. We are then able to describe a finite generating set for K, and hence for G ⊗ G, without needing a polycyclic presentation for ν(G). We apply our results in two ways. We first develop an algorithm that can be implemented within a computer algebra system, such as GAP (Groups, Algorithms and Programming), to compute the nonabelian tensor square of any polycyclic group. Second, we use the commutator calculus and structural results for the cover group ν(G) to directly compute the nonabelian tensor squares for the free nilpotent groups of class 3 and finite rank. The computations for the free nilpotent groups of class 3 were guided by examining the structure of the nonabelian tensor squares of such groups of small rank that were found by computer calculation.
Communications in Algebra, 1995
ABSTRACT Let n be an integer greater than 1, and let G be a group. A subset {x1, X2, ..., xn} of ... more ABSTRACT Let n be an integer greater than 1, and let G be a group. A subset {x1, X2, ..., xn} of n elements of G is said to be rewritable if there are distinct permutations π and σ of {1,2, …, n} such that The group G is said to have the rewriting property Qn or to be n-rewritable, if every subset of n elements of G is rewritable. The main result of this paper shows that the only nontrivial semlsimple groups with the property Q5 are the alternating group A5, the symmetric group S5, the projective special linear group PSL(2, 7) and the projective general linear group PGL(2, 7)
Archiv der Mathematik, 2002
ABSTRACT Let n be an integer greater than 1, and let G be a group. A subset {x1, x2, ..., xn} of ... more ABSTRACT Let n be an integer greater than 1, and let G be a group. A subset {x1, x2, ..., xn} of n elements of G is said to be rewritable if there are distinct permutations $ \pi $ and $ \sigma $ of {1, 2, ..., n} such that¶¶$ x_{\pi(1)}x_{\pi(2)} \ldots x_{\pi(n)} = x_{\sigma(1)}x_{\sigma(2)} \ldots x_{\sigma(n)}. $¶¶A group is said to have the rewriting property Qn if every subset of n elements of the group is rewritable. In this paper we prove that a finite group of odd order has the property Q3 if and only if its derived subgroup has order not exceeding 5.
We study the non-abelian tensor square $G\otimes G$ for the class of groups G that are finitely g... more We study the non-abelian tensor square $G\otimes G$ for the class of groups G that are finitely generated modulo their derived subgroup. In particular, we find conditions on G/G' so that $G\otimes G$ is isomorphic to the direct product of $\nabla(G)$ and the non-abelian exterior square $G\wedge G$. For any group G, we characterize the non-abelian exterior square $G\wedge G$
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Papers by Russell D Blyth