let $g$ be a non-abelian group of order $p^n$‎, ‎where $nleq 5$ in which $g$ is not extra special of order $p^5$‎. ‎in this paper we determine the maximal size of subsets $x$ of $g$‎ ‎with the property that $xyneq yx$ for any $x,y$ in $x$ with‎ ‎$xneq y$‎.

Abstract In this note we realise current algebra with anomalous terms in of a $U(1)$ gauge theory, the space maps $M$ from $S^1$ into compact Lie group corresponding to algebra. The Wilson loop around closed curve is shown be Wess–Zumino–Witten term. This discussion enables simple understanding non-Abelian anomaly Schrödinger picture.

A graph is edge-primitive if its automorphism group acts primitively on the edge set of graph. Edge-primitive graphs form an important subclass symmetric graphs. In this paper, order as a product two distinct primes are completely determined. This depends non-abelian simple groups with subgroup index pq being classified, where p>q odd primes.

We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian ...

A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that (a) every countably infinite abelian torsion group, (b) every abelian torsion group of cardinality greater than continuum, and (c) every (non-trivial) divisible abelian torsion group admits a (Hausdorff) almost maximally almost-periodic gr...

Following partially a suggestion by Pyber, we prove that the diameter of product non-abelian finite simple groups is bounded linearly maximum its factors. For completeness, include case abelian factors and give explicit constants in all bounds.

We say that a group is anti-solvable if all of its composition factors are non-abelian. consider particular family finite groups containing the simple alternating for n≠6 and 26 sporadic groups. prove that, K perfect field X homogeneous space smooth algebraic K-group G with geometric stabilizers lying in this family, then dominated by G-torsor. In particular, G=SL n , such spaces have rational ...

the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...