They have involution centralizers of the form Z / 2Z × PSL ( 2, q ) for q = 3 < sup > n </ sup >, and by investigating groups with an involution centralizer of the similar form Z / 2Z × PSL ( 2, 5 ) Janko found the sporadic group J < sub > 1 </ sub >.
They have involution centralizers of the form Z / 2Z × PSL < sub > 2 </ sub >( q ), and by investigating groups with an involution centralizer of the similar form Z / 2Z × PSL < sub > 2 </ sub >( 5 ) Janko found the sporadic group J < sub > 1 </ sub >.
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