×

zbMATH — the first resource for mathematics

A characterization of \(C_2(q)\) where \(q>5\). (English) Zbl 1068.20020
Summary: The order of every finite group \(G\) can be expressed as a product of coprime positive integers \(m_1,\dots,m_t\) such that \(\pi(m_i)\) is a connected component of the prime graph of \(G\). The integers \(m_1,\dots,m_t\) are called the order components of \(G\). Some non-Abelian simple groups are known to be uniquely determined by their order components. As the main result of this paper, we show that the projective symplectic groups \(C_2(q)\) where \(q>5\) are also uniquely determined by their order components. As corollaries of this result, the validities of a conjecture by J. G. Thompson and a conjecture by W. Shi and J. Bi for \(C_2(q)\) with \(q>5\) are obtained.

MSC:
20D06 Simple groups: alternating groups and groups of Lie type
20D60 Arithmetic and combinatorial problems involving abstract finite groups
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
PDF BibTeX XML Cite
Full Text: EMIS EuDML