given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

We give a classification of maximal elements the set finite groups that can be realized as automorphism polarized abelian threefolds over fields.

We give a classification of maximal elements the set finite groups that can be realized as full automorphism polarized abelian surfaces over fields.

let $g$ be a group and $mathcal{n}$ be the class of all nilpotent groups. a subset $a$ of $g$ is said to be nonnilpotent if for any two distinct elements $a$ and $b$ in $a$, $langle a, brangle notin mathcal{n}$. if, for any other nonnilpotent subset $b$ in $g$, $|a|geq |b|$, then $a$ is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by $ome...

where the matrix in the parenthesis is identically the character table for the cyclic group C3 (group elements vs. irreducible representations). In threefold maximal mixing the CP violation parameter |JCP | is maximal (|JCP | = 1/6 √ 3) and if no two neutrinos are degenerate in mass, CP and T violating asymmetries can approach ±100%. Observables depend on the sqaures of the moduli of the mixing...

background: in this study, the chemical quality of water in some sub-basins of gamasiab river has been investigated for a long term planning of water consuming in the region . methods: the area is about 11 x10 3 km 2 , located in ramadan and kermanshah, the two western regions of iran. in this regard the results of the water samples, which were collected on the outlet of the 13 hydrometrical st...

This paper considers two distinct procedures to lexicographically compose multiple criteria for social or individual decision making. The first procedure composes M binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of the first binary relation, and then within that set, chooses the maximal elements of the second bina...

We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.