A Characterization of Some Finite Simple Groups Through Their Orders and Degree Patterns

作者：Akbari M; Moghaddamfar A R^*; Rahbariyan S

来源：Algebra Colloquium, 2012, 19(3): 473-482.

• prime graph
• degree pattern
• OD-characterizability of a finite group
• simple group

The degree pattern of a finite group G was introduced in [15] and denoted by D(G). A finite group Missaid to be OD-characterizable if G congruent to M for every finite group G such that vertical bar G vertical bar = vertical bar M vertical bar and D(G) = D(M). In this article, we show that the linear groups L-p(2) and Lp+1(2) are OD-characterizable, where 2(p) - 1 is a Mersenne prime. For example, the linear groups L-2(2) congruent to S-3, L-3(2) congruent to L-2(7), L-4(2) congruent to A(8), L-5(2), L-6(2), L-7(2), L-8(2), L-13(2), L-14(2), L-17(2), L-18(2), L-19(2), L-20(2), L-31(2), L-32(2), L-61(2), L-62(2), L-89(2), L-90(2), etc., are OD-characterizable. We also show that the simple groups L-4(5), L-4(7) and U-4(7) are OD-characterizable.

• 出版日期2012-9