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- W2021931421 abstract "A group is 2-generated if it can be generated by two elements x and y. In this case y is called a mate for x. Brenner and Wiegold (1975a Brenner , J. L. , Wiegold , J. ( 1975a ). Two-generator groups. I . Michigan Math. J. 22 : 53 – 64 .[Crossref], [Web of Science ®] , [Google Scholar]) defined a finite group G to have spread r if for every set {x 1, x 2,…, x r } of distinct nontrivial elements of G, there exists an element y ∊ G such that G = 〈 x i , y〉 for all i. A group is said to have exact spread r if it has spread r but not r + 1. The exact spread of a group G is denoted by s(G). Ganief (1996 Ganief , M. S. ( 1996 ). 2-Generations of the Sporadic Simple Groups , Ph.D thesis , University of Natal . [Google Scholar]) in his Ph.D. thesis proved that if G is a sporadic simple group, then s(G) ≥ 2. In Ganief and Moori (2001 Ganief , M. S. , Moori , J. ( 2001 ). On the spread of the sporadic simple groups . Comm. Algebra 29 : 3239 – 3255 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) the second author and Ganief used probabilistic methods and established a reasonable lower bound for the exact spread s(G) of each sporadic simple group G. The present article deals with the search for reasonable upper bounds for the exact spread of the sporadic simple groups." @default.
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- W2021931421 title "On the Exact Spread of Sporadic Simple Groups" @default.
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