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2007•Journal of Chongqing University. English EditionRequires access

A New Characterization of the Finite Orthogonal Simple Group PΩ_(2n)~+(q)

Linhua Zhang

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Abstract

In this paper the authors have proved the following theorem.Let G be a finite group and S be one of finite orthogonal simple groups PΩ22n(q),where n≠ 4,6,8,10,12,14,16.Then G≌S if and only if (i) πe(G)=πe(PΩ+2n(q)),where πe(G) is the set of orders of elements in G;(ii) ord(Snor(G))=ord(Snor(PΩ+2n(q))),where ord(Snor(G)) is the set of orders of normalizers of its Sylow subgroups in G.

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What this paper is about

In this paper the authors have proved the following theorem.Let G be a finite group and S be one of finite orthogonal simple groups PΩ22n(q),where n≠ 4,6,8,10,12,14,16.Then G≌S if and only if (i) πe(G)=πe(PΩ+2n(q)),where πe(G) is the set of orders of elements in G;(ii) ord(Snor(G))=ord(Snor(PΩ+2n(q))),where ord(Snor(G)) is the set of orders of normalizers of its Sylow subgroups in G.

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Available abstract

In this paper the authors have proved the following theorem.Let G be a finite group and S be one of finite orthogonal simple groups PΩ22n(q),where n≠ 4,6,8,10,12,14,16.Then G≌S if and only if (i) πe(G)=πe(PΩ+2n(q)),where πe(G) is the set of orders of elements in G;(ii) ord(Snor(G))=ord(Snor(PΩ+2n(q))),where ord(Snor(G)) is the set of orders of normalizers of its Sylow subgroups in G.

Key concepts: Sylow theorems, Simple group, Mathematics, Finite group, Combinatorics, Simple (philosophy), Group (periodic table), Classification of finite simple groups

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