We introduce interpersonal congruence—the degree to which group members see others in the group as others see themselves—as a moderator of the relationship between diversity and group effectiveness. A longitudinal study of 83 work groups revealed that functional and demographic diversity tended to undermine the functioning of groups with low interpersonal congruence, whereas these detrimental e...

We study congruences on the partial automorphism monoid of a finite rank free group action. determine decomposition congruence this into Rees congruence, Brandt semigroup and an idempotent separating congruence. The constituent parts are further described in terms subgroups direct semidirect products groups. utilize description to demonstrate how number depends

Let n ≥ 2 and Fn be the free group of rank n. Its automorphism group Aut(Fn) has a well-known surjective linear representation ρ : Aut(Fn) −→ Aut(Fn/F ′ n) = GLn(Z) where F ′ n denotes the commutator subgroup of Fn. By Aut (Fn) := ρ(SLn(Z)) we denote the special automorphism group of Fn. For an epimorphism π : Fn → G of Fn onto a finite group G we call Γ(G, π) := {φ ∈ Aut(Fn) | πφ = π} the stan...

The congruence subgroups of the classical modular group which can be defined as the automorphs modulo q of some fixed matrix are studied, and their genera determined. Let T = SL{2, Z). A congruence subgroup of T is any subgroup containing a principal congruence subgroup T^), defined as the set of elements A of T such that A = I mod q, where q is a positive integer. Of these one of the most impo...

A lattice identity is given such that it holds but its dual fails in the normal subgroup lattices of metaabelian groups. Thus the congruence variety of metaabelian groups is not self-dual; this is the first example for a modular congruence variety which is not self-dual. For a ring R with unit element let L(R) denote the class of lattices embeddable in submodule lattices of R-modules. Then HL(R...

Abstract We introduce and study families of finite index subgroups the modular group that generalize congruence subgroups. Such groups, termed ϕ‐congruence subgroups, are obtained by reducing homomorphisms ϕ from into a linear algebraic modulo integers. In particular, we examine two examples, arising on one hand map quasi‐unipotent group, other maps symplectic groups degree four. case, also pro...

Using multilevel structural equations modeling, we examine the extent to which the influence of transformational leadership on work group effectiveness flows through follower perceptions of person-organization or person-supervisor value congruence. Results indicate that the group-level effect of transformational leadership on work group effectiveness was fully accounted for by the group-level i...