Recognizing by Order and Degree Pattern of Some Projective Special Linear Groups

Let M be a finite group and D(M) be the degree pattern of M. Denote by hOD(M) the number of isomorphism classes of finite groups G with the same order and degree pattern as M. A finite group M is called k-fold OD-characterizable if hOD(M) = k. Usually, a 1-fold OD-characterizable group is simply called OD-characterizable. The purpose of this article is twofold. First, it provides some information on the structure of a group from its degree pattern. Second, it proves that the projective special linear groups L4(4), L4(8), L4(9), L4(11), L4(13), L4(16), L4(17) are OD-characterizable.

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