Statistical findings on subgroups belong to the most popular and simple forms of knowledge we encounter in all domains of science, business, or even daily life. We are told such messages as: Unemployment rate is overproportionally high for young men with low educational level, young poor women are infected with AIDS at a much higher rate than their male counterparts, lung cancer mortality rate ...

If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge of N and G/N (see Example 1.1 below), it is nevertheless a standard technique in finite group theory to prove theorems about finite groups by induction on the size of the group and thereby use information about the smaller gro...

Our aim here is to give a fairly self-contained exposition of some basic facts about the Iwahori-Hecke algebra H of a split p-adic group, including Bernstein’s presentation and description of the center, Macdonald’s formula, the CasselmanShalika formula, and the Kato-Lusztig formula. There are no new results here, and the same is essentially true of the proofs. We have been strongly influenced ...

MOTIVATION A number of methods have been developed to predict functional specificity determinants in protein families based on sequence information. Most of these methods rely on pre-defined functional subgroups. Manual subgroup definition is difficult because of the limited number of experimentally characterized subfamilies with differing specificity, while automatic subgroup partitioning usin...

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...