فهرست مقالات Element order

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  1 - تاثیر تعداد عناصر از مرتبه بزرگترین شمارنده اول مرتبه گروه روی ساختار گروه
  علیرضا خلیلی سید صادق صالحی امیری
  فرض کنید S یک گروه ساده غیرآبلی است که با گروه L_2 (r) (جایی که r عدد اول مرسن است) یکریخت نمی باشد. در [1] مورتو حدس زد که اگر گروه متناهی G توسط عناصر از مرتبه p، که در آن p بزرگترین شمارنده اول مرتبه S است تولید شود و تعداد عناصر از مرتبه p درگروههای G وS برابر باشند چکیده کامل

  فرض کنید S یک گروه ساده غیرآبلی است که با گروه L_2 (r) (جایی که r عدد اول مرسن است) یکریخت نمی باشد. در [1] مورتو حدس زد که اگر گروه متناهی G توسط عناصر از مرتبه p، که در آن p بزرگترین شمارنده اول مرتبه S است تولید شود و تعداد عناصر از مرتبه p درگروههای G وS برابر باشند، آن گاه G/(Z(G))≅S . در این مقاله درستی این حدس برای گروههای ساده پراکنده ثابت شده است. پرونده مقاله
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  2 - Characterization of $\mathbf{L_2(p^2)}$ by NSE
  H. Parvizi ‎Mosaed‎‎ A. Tehranian
  Let $G$ be a group and $\pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $nse(G)$ be the set of the number of elements of the same order in $G$. In this paper, we prove that the simple group $L_2(p^2)$ is uniquely determined by $nse(L چکیده کامل

  Let $G$ be a group and $\pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $nse(G)$ be the set of the number of elements of the same order in $G$. In this paper, we prove that the simple group $L_2(p^2)$ is uniquely determined by $nse(L_2(p^2))$, where $p\in\{11,13\}$‎.‎ پرونده مقاله
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  3 - Recognition by prime graph of the almost simple group PGL(2, 25)
  A. Mahmoudifar
  Throughout this paper, every groups are finite. The prime graph of a group $G$ is denotedby $\Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite group $H$ with $\Gamma(H) = \Gamma(G)$, we conclude that $G\cong H$. Until now, it is proved that چکیده کامل

  Throughout this paper, every groups are finite. The prime graph of a group $G$ is denotedby $\Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite group $H$ with $\Gamma(H) = \Gamma(G)$, we conclude that $G\cong H$. Until now, it is proved that if $k$ is an odd numberand $p$ is an odd prime number, then $PGL(2,p^k)$ is recognizable by prime graph. So if $k$ iseven, the recognition by prime graph of $PGL(2,p^k)$, where $p$ is an odd prime number, is anopen problem. In this paper, we generalize this result and we prove that the almost simplegroup $PGL(2,25)$ is recognizable by prime graph. پرونده مقاله
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  4 - On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$
  A. Mahmoudifar
  The prime graph of a finite group $G$ is denoted by$\Gamma(G)$ whose vertex set is $\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a چکیده کامل

  The prime graph of a finite group $G$ is denoted by$\Gamma(G)$ whose vertex set is $\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $\Gamma(H)=\Gamma(G)$, in while $H\not\cong G$. In this paper, we consider finite groups with the same prime graph as the almost simple group $\textrm{PGL}(2,49)$. Moreover, we construct some Frobenius groupswhose prime graphs coincide with $\Gamma(\textrm{PGL}(2,49))$, in particular, we get that $\textrm{PGL}(2,49)$ is unrecognizable by its prime graph. پرونده مقاله
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  5 - A new characterization of chevalley groups $\mathbf{G_2 (q)}$
  B. Ebrahimzadeh A. R. Shabani
  10.30495/jlta.2022.698655
  ‎In this paper‎, ‎we prove that chevalley groups $G_2 (q)$‎, ‎where $q\equiv \pm2($mod 5$)$ and $q^2+q+1$ is a prime number‎, ‎can be uniquely determined by the order of the group and the second largest element order‎.

  ‎In this paper‎, ‎we prove that chevalley groups $G_2 (q)$‎, ‎where $q\equiv \pm2($mod 5$)$ and $q^2+q+1$ is a prime number‎, ‎can be uniquely determined by the order of the group and the second largest element order‎. پرونده مقاله