In groups, an abelian normal subgroup induces congruence. We construct a class of centrally nilpotent Moufang loops containing subloop that does not induce On the other hand, we prove in 6-divisible loops, every congruence solvability adopted from universal-algebraic commutator theory modular varieties is strictly stronger than classical group theory. It open problem whether two notions coincid...

We give an explicit construction for non-congruence subgroups in the fundamental group of a flexible hyperbolic 3-manifold.

Hotzel asks this for semigroups and right congruences; his and the above version are equivalent. Left congruences on M are equivalence relations closed under all left translations; these are thus equivalent to congruences on the free left M -set on one generator. When M is a group, any left congruence is the decomposition of M into the left cosets of some subgroup, so the lattice of left congru...

The scissors congruence conjecture for the unimodular group is an analogue of Hilbert’s third problem, for the equidecomposability of polytopes. Liu and Osserman studied the Ehrhart quasi-polynomials of polytopes naturally associated to graphs whose vertices have degree one or three. In this paper, we prove the scissors congruence conjecture, posed by Haase and McAllister, for this class of pol...

Whether induced-depressed individuals demonstrate a mood congruence effect in unintentional learning is unknown. We manipulated 51 healthy participants into either a happy (n = 25) or a sad mood (n = 26) state and tested their mood-congruent information processing with unintentional learning of negatively charged pictorial stimuli. Participants in the happy mood induction group recognised signi...

Capitalizing upon Implicit Leadership Theories (ILTs) and Leader-member exchange (LMX), this research aims to explore the relationship between the congruence of employees’ ILTs and those traits of their managers and employees’ supportiveness, resistance and behavioral creativity for change. After distributing three questionnaires at three points among teachers, 296 participants completed all th...

In the class of abelian groups a subclass of two-divisible-groups is singled out, and in the latter, a subclass of uniquely-two-divisible-groups. With every such a group a special geometrical structure, more precisely the structure of “congruence of vectors” is correlated. The notion of “affine vector space” (denoted by AffVect) is introduced. This term is defined by means of suitable axiom sys...

INTRODUCTION Cultural congruence is the idea that to the extent a belief or experience is culturally shared it is not to feature in a diagnostic judgement, irrespective of its resemblance to psychiatric pathology. This rests on the argument that since deviation from norms is central to diagnosis, and since what counts as deviation is relative to context, assessing the degree of fit between ment...

This is the latest part of an ongoing project aimed at extending algebraic properties of the classical modular group SL2(Z) to equivalent groups in the theory of Drinfeld modules. We are especially interested in those properties which are important in the classical theory of modular forms. Our results are intended to be applicable to the theory of Drinfeld modular curves and forms. Here we are ...