A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. We compute a mapping class group of a hypekähler manifold M , showing that it is commensurable to an arithmetic lattice in SO(3, b2 − 3). A Teichmüller space of M is a space of complex structures on M up to isotopies. We define a birational Teichmüller space by identifying certain points co...

The usual, or type An, Tamari lattice is a partial order on T A n , the triangulations of an (n+3)-gon. We define a partial order on T B n , the set of centrally symmetric triangulations of a (2n + 2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the An Tamari lattice, and therefore that it deserves to be considered the Bn Tamari lattice. We define a bij...

We describe the normal subgroup lattice of the automorphism groups of the countable universal homogeneous distributive lattice and of the countable atomless generalized Boolean lattice. Also, we show that subgroups of these automorphism groups of index less than 2@0 lie between the pointwise and the setwise stabilizer of a nite set.

Notation and Terminology. Given a finite lattice L, the expression L ∼= [H,G] means “there exist finite groups H < G such that L is isomorphic to the interval {K | H 6 K 6 G} in the subgroup lattice of G.” A group G is called almost simple if G has a normal subgroup S P G which is nonabelian, simple, and has trivial centralizer, CG(S) = (e). If H 6 G, then the core of H in G, denoted coreG(H), ...

Björner [1] showed how a construction by von Neumann of examples of continuous geometries can be adapted to construct a continuous analogue of finite partition lattices. Björner's construction realizes the continuous partition lattice abstractly, as a completion of a direct limit of finite lattices. Here we give an alternative construction realizing a continuous partition lattice concretely as ...

Let G be a linear algebraic group defined over Q, and assume that G(R) is compact and meets every connected component of G(C). Let Q̂ := Ẑ ⊗ Q be the ring of finite adèles. Every arithmetic subgroup Γ of G(Q) is finite, and is obtained by choosing an open, compact subgroup K of G(Q̂) and defining Γ = K ∩G(Q) in G(Q̂). We note that G(Q) is discrete and co-compact in G(Q̂). In this paper, we consider...

in this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $l$-setting. this construction is illustrated by an example. we also prove that for an $l$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $l$-subset provided the given $l$-subset possesses sup-property.

The Chermak–Delgado lattice of a finite group G is self-dual sublattice the subgroup G. In this paper, we focus on groups whose an elementary abelian p-group. We prove that such are nilpotent class 2. also that, for any p-group E, there exists E.