منابع مشابه
The Higher Commutator Subgroups of a Group
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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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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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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متن کاملCommutator Theory for Loops
Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the congruence commutator to generators of the total inner mapping group. We specialize the fundamental theorem into several varieties of loops, and also discus...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1931
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.17.3.144