We study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms. We show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry, in particular the moduli of K3 surfaces. We give applications to modular forms and to computing the fundamental groups of some moduli spaces. Many moduli space...

In this paper we continue the study of intuitionistic fuzzy groups by introducing the notion of intuitionistic fuzzy normal subgroup based on intuitionistic fuzzy space as a generalization of fuzzy normal subgroup. MSC2000 : 20N25, 03E72. Key Word : Fuzzy space, intuitionistic fuzzy space, intuitionistic fuzzy group, normal intuitionistic fuzzy subgroup .

The goal of this survey is to study some classes of groups determined by different types of complementation of their normal subgroup lattices. The groups whose normal subgroup lattices are Stone lattices, boolean lattices or ortholattices will be also investigated. MSC (2000): Primary 20D30, Secondary 20E15, 06C15, 06D15.

Abstract We prove that a group homomorphism ? : L ? G \varphi\colon L\to G from locally compact Hausdorff ???? into discrete ???? either is continuous, or there exists normal open subgroup N ? N\subseteq L such ?</m:m...

We prove that Morse local-to-global groups grow exponentially faster than their infinite-index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the context quasi-convex subgroups hyperbolic to broad class contains mapping group, CAT(0) groups, fundamental closed 3-manifolds. To accomplish this, we develop theory automatic structures on geodesics groups. Other applicati...

A set of the form C-Z ; where CDR is convex and Z denotes the integer lattice, is called a convex lattice set. It is known that the Helly number of d-dimensional convex lattice sets is 2 : We prove that the fractional Helly number is only d þ 1: For every d and every aAð0; 1 there exists b40 such that whenever F1;y;Fn are convex lattice sets in Z such that T iAI Fia| for at least að n dþ1Þ inde...