Let V be a finite dimensional complex linear space and let G be an irreducible finite subgroup of GL(V ). For a G-invariant lattice Λ in V of maximal rank, we give a description of structure of the complex torus V/Λ. In particular, we prove that for a wide class of groups, V/Λ is isogenous to a self-product of an elliptic curve, and that in many cases V/Λ is isomorphic to a product of mutually ...

This Heisenberg group is a 2-step nilpotent Lie group and is important in the study of toroidal compactifications of Siegel moduli spaces. In fact, H (g,h) R is obtained as the unipotent radical of the parabolic subgroup of Sp(g+h,R) associated with the rational boundary component Fg ( cf. [F-C] p. 123 or [N] p. 21 ). For the motivation of the study of this Heisenberg group we refer to [Y4]-[Y8...

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, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

Abstract We study local models that describe the singularities of Shimura varieties non-PEL type for orthogonal groups at primes where level subgroup is given by stabilizer a single lattice. In particular, we use Pappas–Zhu construction and give explicit equations an open subset around “worst” point These display affine chart model as hypersurface in determinantal scheme. Using this, prove spec...

Let o(G) be the average of element orders a finite group G. A research topic concerning this quantity is understanding relation between and o(H), where H subgroup N class nilpotent groups let L(G) lattice In paper, we show that set {o(G)o(H) | G∈N,H∈L(G)} dense in [0,∞). Other density results are outlined throughout paper.

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.