A Characterization of Some Finite Simple Groups Through Their Orders and Degree Patterns
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The degree pattern of a finite group G was introduced in [15] and denoted by D (G). A finite group M is said to be OD-characterizable if G ≅ M for every finite group G such that |G|=|M| and D (G)= D (M). In this article, we show that the linear groups Lp(2) and Lp+1(2) are OD-characterizable, where 2p-1 is a Mersenne prime. For example, the linear groups L2(2) ≅ S3, L3(2) ≅ L2(7), L4(2) ≅ A8, L5(2), L6(2), L7(2), L8(2), L13(2), L14(2), L17(2), L18(2), L19(2), L20(2), L31(2), L32(2), L61(2), L62(2), L89(2), L90(2), etc., are OD-characterizable. We also show that the simple groups L4(5), L4(7) and U4(7) are OD-characterizable.
2009 ◽
Vol 19
(07)
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pp. 873-889
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1998 ◽
Vol 58
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pp. 137-145
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2013 ◽
Vol 834-836
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pp. 1799-1802
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2016 ◽
Vol 15
(09)
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pp. 1650163
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2016 ◽
Vol 09
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pp. 1650054