ﻻ يوجد ملخص باللغة العربية
Let $G$ be a nonabelian group, $Asubseteq G$ an abelian subgroup and $ngeqslant 2$ an integer. We say that $G$ has an $n$-abelian partition with respect to $A$, if there exists a partition of $G$ into $A$ and $n$ disjoint commuting subsets $A_1, A_2, ldots, A_n$ of $G$, such that $|A_i|>1$ for each $i=1, 2, ldots, n$. We first classify all nonabelian groups, up to isomorphism, which have an $n$-abelian partition for $n=2, 3$. Then, we provide some formulas concerning the number of spanning trees of commuting graphs associated with certain finite groups. Finally, we point out some ways to finding the number of spanning trees of the commuting graphs of some specific groups.
In this article we give an expository account of the holomorphic motion theorem based on work of M`a~ne-Sad-Sullivan, Bers-Royden, and Chirka. After proving this theorem, we show that tangent vectors to holomorphic motions have $|epsilon log epsilon|
We study a curious class of partitions, the parts of which obey an exceedingly strict congruence condition we refer to as sequential congruence: the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part congruent to zero mo
We study partial homology and cohomology from ring theoretic point of view via the partial group algebra $mathbb{K}_{par}G$. In particular, we link the partial homology and cohomology of a group $G$ with coefficients in an irreducible (resp. indecomp
In this article, we shall explore the constructions of Bernstein sets, and prove that every Bernstein set is nonmeasurable and doesnt have the property of Baire. We shall also prove that Bernstein sets dont have the perfect set property.
Due to the discovery of the hidden-charm pentaquark $P_c$ states by the LHCb collaboration, the interests on the candidates of hidden-bottom pentaquark $P_b$ states are increasing. They are anticipated to exist as the analogues of the $P_c$ states in