Let G be a group with cyclic commutator subgroup of order p and F a field of characteristic p. We obtain the description of the group algebras FG of Lie derived length 3.

We give an algorithm that decides whether a single equation in group is virtually class $2$ nilpotent with cyclic commutator subgroup, such as the Heisenberg group, admits solution. This generalises work of Duchin, Liang and Shapiro to finite extensions.

in the San Gabriel and the San Gorgonio mountains about 40 and 90 miles to the east. But when it comes to matching the Glacial epochs of the coast with those of the Sierra Nevada as lately studied by Blackwelder,3 or of the northeastern United States, difficulty is encountered. A simple solution of the difficulty would be to equate the Budu coastal epoch with the next-to-last Glacial epoch, the...

The commutator length “cl G ” of a group G is the least natural number c such that every element of the derived subgroup of G is a product of c commutators. We give an upper bound for cl G when G is a d-generator nilpotent-by-abelian-by-finite group. Then, we give an upper bound for the commutator length of a soluble-by-finite linear group over C that depends only on d and the degree of lineari...

The residual finiteness of the class of groups of fibred knots, or those knot groups with finitely generated and, therefore, free commutator subgroups, has been known for some time. Using Baumslag's results on absolutely parafree groups, this paper extends the result to twist knots (Whitehead doubles of the trivial knot) and certain other classes of nonfibred knots whose minimal spanning surfac...

The residual finiteness of the class of groups of fibred knots, or those knot groups with finitely generated and, therefore, free commutator subgroups, has been known for some time. Using Baumslag's results on absolutely parafree groups, this paper extends the result to twist knots (Whitehead doubles of the trivial knot) and certain other classes of nonfibred knots whose minimal spanning surfac...

Definitions and classifications of reduced surds for non-arithmetical groups on the hyperbolic plane is proposed, as well those some congruence subgroups. The considered are desymmetrized group, its Γ0 subgroup, a generalized Hecke group according choice commutator subgroup group. definitions studied to ordering generators conjugacy subclasses groups. construction tori defined obtained after te...

Let m,n be positive integers, v a multilinear commutator word and w = vm. We prove that if G is a residually finite group in which all wvalues are n-Engel, then the verbal subgroup w(G) is locally nilpotent. We also examine the question whether this is true in the case where G is locally graded rather than residually finite. We answer the question affirmatively in the case where m = 1. Moreover...

D. Epstein has shown [1] that for quite general groups of homeomorphisms, the commutator subgroup is simple. In particular, let M be a manifold. (In this note, we assume all manifolds are finite dimensional, Hausdorff, class C, and have a countable basis for their topology.) By a C r + mapping (resp. diffeomorphism) we mean a C mapping (resp. diffeomorphism) whose rth derivative is Lipschitz. L...