List of Articles Element order

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  1 - The influence of the number of elements of prime order on the structure of finite groups
  Alireza Khalili Asboei Seyed Sadegh Salehi Amiri
  Let G be a finite group. We denote by n_{p}(G) the number of Sylow p-subgroup of G, that is, n_{p}(G)=|mathrm{Syl}_{p}(G)|. Denoted by m_{i}(G) the number of elements of order i of G.Given a positive integer n and a prime r, we write n_{r} to denote thefull r-part of n, More

  Let G be a finite group. We denote by n_{p}(G) the number of Sylow p-subgroup of G, that is, n_{p}(G)=|mathrm{Syl}_{p}(G)|. Denoted by m_{i}(G) the number of elements of order i of G.Given a positive integer n and a prime r, we write n_{r} to denote thefull r-part of n, so we can factor n=n_{r}m, where m is not divisibleby r.Now fix a prime p. We say that a positive integer n is a strong Sylow number for $p$ if for every prime q, the full q-part n_{q} of n satisfies n_{q}equiv 1 (mod p). Note that if n is a strong Sylownumber for p, then nequiv 1 (mod p), and thus n is not divisible by p. Note also that the set of strong Sylow numbers for p is closed undermultiplication.Let S be a nonabelian simple group that is not isomorphic to L_2 (r), where r is a Mersenne prime and let p be the greatest prime divisor of |S|. In [1, Conjecture E] A. Moreto conjectured that if a finite group G is generated by elements of order p and G has the same number of elements of order p as S, then G/(Z(G))≅S. In this paper, we verify the conjecture for the sporadic simple groups. Manuscript profile
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  2 - Characterization of $\mathbf{L_2(p^2)}$ by NSE
  H. Parvizi ‎Mosaed‎‎ A. Tehranian
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  3 - Recognition by prime graph of the almost simple group PGL(2, 25)
  A. Mahmoudifar
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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
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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
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