Characterization of G 2(q), where 2 &lt; q ≡ −1(mod 3), by order components

Nosratpour, P.; Darafsheh, M. R.

doi:10.1134/s0037446613050121

Cited by 2 publications

(4 citation statements)

References 14 publications

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“…Thus, the hypothesis that |G| = |G 2 (11)| yields G and G 2 (11) having the same set of order components. Now, by the Main Theorem in [7], G is isomorphic to S, as required.…”

Section: Proof Of Theorem Amentioning

confidence: 98%

“…We denote by OC(G) the set of order components of G. The group M is said to be characterizable by order component if, for every finite group G, the equality OC(G) = OC(M ) implies the group isomorphism G ∼ = M . It has already been shown that many simple groups are characterizable by order component (for instance, see [1,2,7]). Therefore, when under the conditions |G| = |M | and D(G) = D(M ) we can conclude that OC(G) = OC(M ), and M is characterizable by order component, it follows that M is ODcharacterizable too.…”

Section: Some Remarksmentioning

confidence: 99%

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An OD-characterizable class of simple groups

Akbari

Chen

Moghaddamfar

2020

ADM

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“…Thus, the hypothesis that |G| = |G 2 (11)| yields G and G 2 (11) having the same set of order components. Now, by the Main Theorem in [7], G is isomorphic to S, as required.…”

Section: Proof Of Theorem Amentioning

confidence: 98%

Section: Some Remarksmentioning

confidence: 99%

An OD-characterizable class of simple groups

Akbari

Chen

Moghaddamfar

2020

ADM

View full text Add to dashboard Cite

show abstract

Section: Some Remarksmentioning

confidence: 99%

“…Thus, the hypothesis that |G| = |G 2(11)| yields G and G 2(11) having the same set of order components. Now, by the Main Theorem in[7], G is isomorphic to S, as required. Using similar arguments to those in the previous case, one can show that K is a {7, 19, 37} ′ -group and G is isomorphic to G 2(11).…”

mentioning

confidence: 97%

An OD-Characterizable Class of Simple Groups

Akbari¹,

Chen²,

Moghaddamfar³

2018

Preprint

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It is proved that finite nonabelian simple groups S with max π(S) = 37 are uniquely determined by their order and degree pattern in the class of all finite groups. IntroductionThroughout this note, all the groups under consideration are finite, and simple groups are nonabelian. Given a group G, the spectrum ω(G) of G is the set of orders of elements in G. Clearly, the spectrum ω(G) is closed and partially ordered by the divisibility relation, and hence is uniquely determined by the set µ(G) of its elements which are maximal under the divisibility relation.One of the most well-known graphs associated with G is the prime graph (or Gruenberg-Kegel graph) denoted by GK(G). The vertices of GK(G) are the prime divisors of |G| and two distinct vertices p and q are joined by an edge (written by p, where d G (p i ) denotes the degree of p i in the prime graph GK(G). We call this k-tuple D(G) the degree pattern of G. In addition, we denote by OD(G) the set of pairwise non-isomorphic finite groups with the same order and degree pattern as G, and put h(G) = |OD(G)|. Since there are only finitely many isomorphism types of groups of order |G|, 1 h(G) < ∞. Now, we have the following definition.Usually, a 1-fold ODcharacterizable group is simply called OD-characterizable, and it is called quasi OD-characterizable if it is k-fold OD-characterizable for some k > 1.

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Characterization of G 2(q), where 2 < q ≡ −1(mod 3), by order components

Cited by 2 publications

References 14 publications

An OD-characterizable class of simple groups

An OD-characterizable class of simple groups

An OD-Characterizable Class of Simple Groups

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