rX-Complementary generations of the janko groups j1 J2 And j3 |
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Authors: | Shahiem Ganief Jamshid Moori |
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Affiliation: | 1. University of the Western Cape , Private Bag XI7, Bellville, 7535, South Africa E-mail: mganief@math.uwc.ac.za;2. University of Natal , Private Bag X01, Scottsville, Pietermaritzburg, 3209, South Africa E-mail: moon@unpsunJ.cc.unp.ac.za |
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Abstract: | A finite group G with conjugacy class rX is said to be rX-complementary generated if, given an arbitrary x∈G-1, there is a y ∈ rXsuch that G (x,y). The rX-complementary generation of the simple groups was first introduced by Woldar in [17] to show that every sporadic simple group can be generated by an arbitrary element and another suitable element. It is conjectured in [5] that every finite simple group can be generated in this way. In this paper we investigate the rX-complementary generation of the first three Janko groups in an attemp to further develop the techniques of finding rX-complementary generation of the finite simple groups. As a consequence, we obtained all the(p,q,r)-generations of the Janko group J 3, where p,q,r are distinct primes. |
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