Compute the center Z of SL2(Z/p)

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Compute the center Z of SL2(Z/p)

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We consider the discrete Heisenberg group G Heis3 Z whichis the group of matrices of the form where a b c are from Z We can consider also the group G as aset of all integer triples endowed with the group law a1 b1c1a2 b2 c2 a1 a2 b1 b2 c1 c2 a1b2 1It is clear that 1 0 00 1 0 0 0 1 and the groupG is generated by the elements 1 0 0 and 0 0 1 Let AutG be the group of automorphisms of the group G Thestarting point for this note was the group homomorphism Z AutGconstructed in 3 5 and given by the formulaRda b c 2where Rd is the automorphism of the group G induced by anelement d Z Formula 2 was obtained in 3 after somecalculation of automorphisms which See Answer

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Compute the center Z of SL2(Z/p)

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Compute the center Z of SL2(Z/p)

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