Thompson’s conjecture for the alternating group of degree 2 p and 2 p + 1

Azam Babai; Ali Mahmoudifar

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 4, page 1049-1058
  • ISSN: 0011-4642

Abstract

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For a finite group G denote by N ( G ) the set of conjugacy class sizes of G . In 1980s, J. G. Thompson posed the following conjecture: If L is a finite nonabelian simple group, G is a finite group with trivial center and N ( G ) = N ( L ) , then G ≅ L . We prove this conjecture for an infinite class of simple groups. Let p be an odd prime. We show that every finite group G with the property Z ( G ) = 1 and N ( G ) = N ( A i ) is necessarily isomorphic to A i , where i ∈ { 2 p , 2 p + 1 } .

How to cite

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Babai, Azam, and Mahmoudifar, Ali. "Thompson’s conjecture for the alternating group of degree $2p$ and $2p+1$." Czechoslovak Mathematical Journal 67.4 (2017): 1049-1058. <http://eudml.org/doc/294402>.

@article{Babai2017,
abstract = {For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N(G) = N(L)$, then $G\cong L$. We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z(G)=1$ and $N(G) = N(A_\{i\})$ is necessarily isomorphic to $A_\{i\}$, where $i\in \lbrace 2p,2p+1\rbrace $.},
author = {Babai, Azam, Mahmoudifar, Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite group; conjugacy class size; simple group},
language = {eng},
number = {4},
pages = {1049-1058},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Thompson’s conjecture for the alternating group of degree $2p$ and $2p+1$},
url = {http://eudml.org/doc/294402},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Babai, Azam
AU - Mahmoudifar, Ali
TI - Thompson’s conjecture for the alternating group of degree $2p$ and $2p+1$
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 1049
EP - 1058
AB - For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N(G) = N(L)$, then $G\cong L$. We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z(G)=1$ and $N(G) = N(A_{i})$ is necessarily isomorphic to $A_{i}$, where $i\in \lbrace 2p,2p+1\rbrace $.
LA - eng
KW - finite group; conjugacy class size; simple group
UR - http://eudml.org/doc/294402
ER -

References

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