Volume 2, Issue 4
مرور بر اساس
ارسال های اخیر
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On the probability of being a $2$-Engel group
(University of Isfahan, 2013-12-01)Let $G$ be a finite group and $d_2(G)$ denotes the probability that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $G$. We will obtain lower and upper bounds for $d_2(G)$ in the case where the sets $E_G(x)={yin ...
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The $n$-ary adding machine and solvable groups
(University of Isfahan, 2013-12-01)We describe under various conditions abelian subgroups of the automorphism group $mathrm{Aut}(T_{n})$ of the regular $n$-ary tree $T_{n}$, which are normalized by the $n$-ary adding machine $tau =(e, dots, e,tau ...
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On finite C-tidy groups
(University of Isfahan, 2013-12-01)A group $G$ is said to be a C-tidy group if for every element $x in G setminus K(G)$, the set $Cyc(x)=lbrace y in G mid langle x, y rangle ; {rm is ; cyclic} rbrace$ is a cyclic subgroup of $G$, where $K(G)=underset{x ...
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Noninner automorphisms of finite $p$-groups leaving the center elementwise fixed
(University of Isfahan, 2013-12-01)A longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$. Let $G$ be a finite nonabelian $p$-group. It is known that if $G$ is regular or of nilpotency class $2$ ...
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Unit group of algebra of circulant matrices
(University of Isfahan, 2013-12-01)Let $Cr_n(F_p)$ denote the algebra of $n times n$ circulant matrices over $F_p$, the finite field of order $p$ a prime. The order of the unit groups $mathcal{U}(Cr_3(F_p))$, $mathcal{U}(Cr_4(F_p))$ and ...
