Groups with identities

This is a survey of a still evolving subject. The purpose is to develop a theory of prounipotent (respectively pro-$p$) groups satisfying a prounipotent (respectively pro-$p$) identity that is parallel to the theory of PI-algebra

Why Trust Out-groups? The Role of Punishment Under Uncertainty

We conducted a hidden-effort trust game, in which we assigned subjects to one of two groups. The groups, which were formed through two different group formation processes, included a “social” group that required sharing and exchange among its members, and a “non-social” group that did not. Once assigned, subjects participated in the game with members from both groups, either with or without the opportunity to punish a trustee who may have defected on them. We found that for investors in the non-social group, the opportunity to punish a trustee worked to promote trust, but only when the trustee was a member of the other group. For the social group, the opportunity to punish had no effect on the investors’ trust decisions, regardless of the trustee\u27s group. We provide a theoretical framework to explain this asymmetric effect of punishment on trust. Our results suggest that groups with identities founded in sharing and exchange—a feature of globalized societies—may find it less necessary to engage in costly punishment. As a result, they may enjoy gains in economic efficiency

Gay men, Gaydar and the commodification of difference

Purpose To investigate ICT mediated inclusion and exclusion in terms of sexuality through a study of a commercial social networking website for gay men Design/methodology/approach The paper uses an approach based on technological inscription and the commodification of difference to study Gaydar, a commercial social networking site. Findings Through the activities, events and interactions offered by Gaydar, we identify a series of contrasting identity constructions and market segmentations which are constructed through the cyclic commodification of difference. These are fuelled by a particular series of meanings attached to gay male sexualities which serve to keep gay men positioned as a niche market. Research limitations/implications The research centres on the study of one, albeit widely used, website with a very specific set of purposes. The study offers a model for future research on sexuality and ICTs. Originality/value This study places sexuality centre stage in an ICT mediated environment and provides insights into the contemporary phenomenon of social networking. As a sexualized object, Gaydar presents a semiosis of politicized messages that question heteronormativity while simultaneously contributing to the definition of an increasingly globalized, commercialized and monolithic form of gay male sexuality defined against ICT

Minimal conditions on Clifford semigroup congruences

A known result in groups concerning the inheritance of minimal conditions on normal subgroups by subgroups with finite indexes is extended to semilattices of groups [E(S),Se,ϕe,f] with identities in which all ϕe,f are epimorphisms (called q partial groups). Formulation of this result in terms of q congruences is also obtained

A STUDY ON PERMUTATION GROUP

In this paper we introduced what is meant by a permutation on a given set and showed how they form a group. We discussed the cycle notation of permutation and how it is useful in determining various properties of permutation groups. In fact it is shown that a permutation can be decomposed into disjoint cycles uniquely and that order of the permutation is the l.c.m of the lengths of the cycle in a decomposition of disjoint cycles

New-type Quasirandom Groups and Applications

This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we provide conditions such that one can find tuples $(x_0, \ldots, x_k)\in X^{k+1}$ satisfying $x_1x_2\ldots x_k=x_0$ or conditions to guarantee that the product set $XX$ grows exponentially. In a special case of the group of rigid-motions in the plane over an arbitrary finite field, our results offer a reasonably complete description of structures of this group.Comment: V2: references update