Note on commutator subgroups of factorisable groups
نویسندگان
چکیده
منابع مشابه
On 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...
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Artin groups (also known as Artin-Tits groups) are generalizations of Artin’s braid groups. This paper concerns Artin groups of spherical type, that is, those whose corresponding Coxeter group is finite, as is the case for the braid groups. We compute presentations for the commutator subgroups of the irreducible spherical-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the b...
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it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...
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It is not the object of this address to introduce you to new theories or to tell of great discoveries. Quite on the contrary; I intend to speak of unsolved problems and of conjectures. In order to describe these, certain concepts will have to be discussed ; and for obtaining a proper perspective it will be necessary to mention a number of theorems, some of them new. The proofs of the latter wil...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1955
ISSN: 0386-2194
DOI: 10.3792/pja/1195525588