Finite groups with a standard-component of type \(L_ 3(4)\). II (Q1059145)

This paper closes the investigation of the authors on the \(''L_ 3(4)\)- type standard-subgroup problem'', which was begun in [ibid. 65, 59-75 (1981; Zbl 0478.20014)]. Here the authors consider the following situation: A is a standard subgroup of a finite simple group G with \(A/Z(A)\simeq L_ 3(4)\). The case is treated, where Z(A) contains a nontrivial 2-part of the Schur multiplier of \(L_ 3(4)\) i.e. \(| Z(A)|\) is even. As the main result of this part on the work on the \(''L_ 3(4)\)-component problem'' one has: If the 2-rank of Z(A) is one, then \(G\simeq ON\) (the O'Nan simple group). The proof is based on a very detailed and complex analysis of the structure of \(N_ G(A)\).