Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک ایرانیان IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 7 14 8888 13 en jalali 1394 1 1 gregorian 2015 4 1 10 1 online 1 fulltext
en OD-characterization of Almost Simple Groups Related to displaystyle D4(4) تخصصي Special پژوهشي Research paper Let \$G\$ be a finite group and \$pi_{e}(G)\$ be the set of orders of all elements in \$G\$. The set \$pi_{e}(G)\$ determines the prime graph (or Grunberg-Kegel graph) \$Gamma(G)\$ whose vertex set is \$pi(G)\$, the set of primes dividing the order of \$G\$, and two vertices \$p\$ and \$q\$ are adjacent if and only if \$pqinpi_{e}(G)\$. The degree \$deg(p)\$ of a vertex \$pin pi(G)\$, is the number of edges incident on \$p\$. Let \$pi(G)={p_{1},p_{2},...,p_{k}}\$ with \$p_{1}<p_{2}<...<p_{k}\$. We define \$D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))\$, which is called the degree pattern of \$G\$. The group \$G\$ is called \$k\$-fold OD-characterizable if there exist exactly \$k\$ non-isomorphic groups \$M\$ satisfying conditions \$|G|=|M|\$ and \$D(G)=D(M)\$. Usually a 1-fold OD-characterizable group is simply called OD-characterizable. In this paper, we classify all finite groups with the same order and degree pattern as an almost simple groups related to \$D_{4}(4)\$. Degree pattern, \$k\$-fold OD-characterizable, Almost simple group. 23 43 http://ijmsi.ir/browse.php?a_code=A-10-415-1&slc_lang=en&sid=1 G. R. Rezaeezadeh rezaeezadeh@sci.sku.ac.ir `10031947532846001917` 10031947532846001917 Yes university of shahrekord M. R. Darafsheh darafsheh@ut.ac.ir `10031947532846001918` 10031947532846001918 No university of tehran M. Bibak m.bibak62@gmail.com `10031947532846001919` 10031947532846001919 No university of shahrekord M. Sajadi sajadi−mas@yahoo.com `10031947532846001920` 10031947532846001920 No university of shahrekord