منابع مشابه
Associativity of the Commutator Operation in Groups
The study of associativity of the commutator operation in groups goes back to the work of F. W. Levi in 1942. In the 1960’s Richard J. Thompson created a group F whose elements are representatives of the generalized associative law for an arbitrary binary operation. In 2006, Geoghegan and Guzmán proved that a group G is solvable if and only if the commutator operation in G eventually satisfies ...
متن کاملgroups with minimax commutator subgroup
a result of dixon, evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $g$ itself has this property, i.e. the commutator subgroup of $g$ has finite rank. it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup, then also the commutator s...
متن کاملOn Symmetric Commutator Subgroups, Braids, Links and Homotopy Groups
In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for br...
متن کاملCommutator Length of Finitely Generated Linear Groups
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...
متن کاملRelative Commutator Theory in Varieties of Ω-groups
We introduce a new notion of commutator which depends on a choice of subvariety in any variety of Ω-groups. We prove that this notion encompasses Higgins’s commutator, Fröhlich’s central extensions and the Peiffer commutator of precrossed modules.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1988
ISSN: 0263-6115
DOI: 10.1017/s1446788700032304