N-ary Groups Research Articles

On Permutable Subgroups of n-ary Groups

On Permutable Subgroups of n-ary Groups

On Rusakov's n-ary rs-Groups

Properties of n-ary groups connected with the affine geometry are considered. Some conditions for an n-ary rs-group to be derived from a binary group are given. Necessary and sufficient conditions for an n-ary group \(\left\langle {\theta ,b} \right\rangle \)-derived from an additive group of a field to be an rs-group are obtained. The existence of non-commutative n-ary rs-groups which are not derived from any group of arity m 2 is proved.

On τ-Closed Formations of n-Ary Group

We prove that if G is a nonsingle-element n-ary finite group that belongs to a τ-closed formation \(\mathfrak{F}\), then \(G/{\text{soc(}}G{\text{)}} \in \Phi _\tau (\mathfrak{F})\), where \(\Phi _\tau (\mathfrak{F})\) is the intersection of all maximal τ-closed subformations of the τ-closed formation of n-ary groups \(\mathfrak{F}\).

Generalized morphisms of abelian n-ary groups

Generalized morphisms of abelian n-ary groups

Sylow Structure of Idempotent n-Ary Groups

We study idempotent n-ary groups. We describe the Sylow structure of finite idempotent n-ary groups.

Balanced identity that describes n-ary group isotopes in the class of all n-ary quasigroups

We obtain a balanced identity that holds in a primitive n-ary quasigroup if and only if the polyadic quasigroup associated with the considered primitive n-ary quasigroup is a polyadic group isotope.

Towards a taxonomy of CIM activities

The need for a taxonomy of CIM activities is introduced as a basic requirement to facilitate mutual understanding among the members of multidiscipli nary groups involved in CIM. A preliminary proposal for such a taxonomy is presented, mainly as a starting platform to promote discussion and to act as a catalyzer towards the achievement of a truly comprehensive taxonomy of CIM activities.

Editor's Introduction. Special Feature: UCLA French Department Symposium--Generative Anthropology: Origin and Representation

UCLA French Department Generative Anthropology: Origin and Representation Symposium Cathryn Brimhall Editor, Paroles Gelees group of pre-hiinians (perhaps following a hunting expedition) sur- round an object that strongly excites their appetite (perhaps a large edible animal that has just succumbed to their blows). Everyone is pre- paring to move toward the object. But each, noticing the appropria- tive niovemetit of the others, and intimidated by the scene's potential for violent conflict, aborts his gesture. This aborted gesture, directed toward the central object, and consequently reinforcing the attention that all already it. A bestow on it, functions as an ostensive designation of that, for a certain For as soon as everyone notices time at least, no one will seek to appropriate the object, each understands the others' gesture as meaning the object. The scene will remain in their as centered memory on an object that so excites their appetite that it paradoxi- cally becomes for that very reason untouchable. The aborted gesture of the mdividuals on the periphery, which is prolonged in the kinetic unagination of each toward the object, becomes the sign of the object. The reproduction of it this sign not only evokes the object but designates is to the other participants of the scene. This gesture its thus the first act of representation, and collective performafice constitutes the origi- its nary group as a huirian coniniunity bound together by servation of the ethical constraint realized gesture/sign for the act of appropriation. in the cotnmon ob- substitution of the — Originary Introduction, Hypothesis. Unpublished summary from Eric Cans' The Promise of Generative Anthropology.