A regular map M is a cellular decomposition of a surface such that its automorphism group Aut(M) acts transitively on the flags of M. It can be shown that if a Sylow subgroup P ≤ Aut(M) has order coprime to the Euler characteristic of the supporting surface, then P is cyclic or dihedral. This observation motivates the topic of the current paper, where we study regular maps whose automorphism gr...

First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χH, χHc) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating cong...

BACKGROUND Although allergen avoidance is known to be important for treating atopic diseases, there is a very limited amount of time for clinical education of patients on this topic. METHODS We compared the effect of the thorough home visit counseling (>60 minutes per visit) for avoiding house dust mites (HDMs) with that of regular guidance in our clinics (10 minutes per patient). We enrolled...

A graph $X$ is defined inductively to be $(a_0,\dots,a_{n-1})$-regular if $a_0$-regular and for every vertex $v$ of $X$, the sphere radius $1$ around an $(a_1,\dots,a_{n-1})$-regular graph. Such a said highly regular (HR) level $n$ $a_{n-1}\neq 0$. Chapman, Linial Peled studied HR-graphs 2 provided several methods construct families graphs which are expanders globally locally. They ask whether ...

The affine general linear group acting on a vector space over prime field is well-understood mathematical object. Its elementary abelian regular subgroups have recently drawn attention in applied mathematics thanks to their use cryptography as way hide or detect weaknesses inside block ciphers. This paper focused building convenient representation of elements which suits better the purposes cry...

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

We prove that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property we show that almost all finite subsets of the group generate free subgroups. We derive consequences of these theorems on Thompson’s group F , weakly branch groups, automorphism groups of regular trees and profinite gr...