A053725
Number of n X n binary matrices of order dividing 3 (also number of solutions to X^3=I in GL(n,2)).
Original entry on oeis.org
1, 3, 57, 1233, 75393, 19109889, 6326835201, 6388287561729, 23576681450405889, 120906321631678693377, 1968421511613895105052673, 111055505036706392268074909697, 8965464105556083354144035638870017
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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\\ See Morison theorem 2.6
\\ F(n,q,k) is number of solutions to X^k=I in GL(i, GF(q)) for i=1..n.
\\ q is power of prime and gcd(q, k) = 1.
B(n,q,e)={sum(m=0, n\e, x^(m*e)/prod(k=0, m-1, q^(m*e)-q^(k*e)))}
F(n,q,k)={if(gcd(q,k)<>1, error("no can do")); my(D=ffgen(q)^0); my(f=factor(D*(x^k-1))); my(p=prod(i=1, #f~, (B(n, q, poldegree(f[i,1])) + O(x*x^n))^f[i,2])); my(r=B(n,q,1)); vector(n, i, polcoeff(p, i)/polcoeff(r, i))}
F(10, 2, 3) \\ Andrew Howroyd, Jul 09 2018
A062250
Number of cyclic subgroups of Chevalley group A_n(2) (the group of nonsingular n X n matrices over GF(2) ).
Original entry on oeis.org
1, 5, 79, 6974, 2037136, 2890467344, 14011554132032, 325330342132674560, 27173394819858612320256, 10158190320726534408118452224, 13156630408268153048253765001412608, 80280189722884518774834501142737770774528
Offset: 1
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 01 2001
a(3) = 1/phi(1)+21/phi(2)+56/phi(3)+42/phi(4)+48/phi(7) = 79.
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053851
Number of n X n matrices over GF(3) of order dividing 6 (i.e., number of solutions of X^6=I in GL(n,3)).
Original entry on oeis.org
2, 30, 3564, 2591892, 13309150824, 472846514324760, 66010378571766577008, 57420388405507315431721104, 346655903509457555048839231419168, 13346176825705020413432642810638228113120, 3550829168059531965851571481124814713651514707136
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053861
Number of n X n matrices over GF(4) of order dividing 6 (i.e., number of solutions of X^6=I in GL(n,4)).
Original entry on oeis.org
3, 108, 39924, 168448464, 7334262484992, 3386694351039040512, 10641273426523761445748736, 340916846631327852552215693623296, 114528491766510715239712268894889666674688, 431116212874608758195979601409742939536338628640768
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053876
Number of elements of order 6 in GL(n,2).
Original entry on oeis.org
0, 0, 0, 5040, 1249920, 1315915776, 2224389629952, 13813319064330240, 219415609610739548160, 16360077906225109102362624, 3333279237117892795069534568448, 2704161159785811615896281588873297920
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
Showing 1-5 of 5 results.
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