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Enumerating algebras over a finite field | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 2، شماره 3، آذر 2013، صفحه 49-61 اصل مقاله (282.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2440 | ||
| نویسنده | ||
| Michael Vaughan-Lee* | ||
| Oxford University Mathematical Institute | ||
| چکیده | ||
| We obtain the PORC formulae for the number of non-associative algebras of dimension 2, 3 and 4 over the finite field GF$(q)$. We also give some asymptotic bounds for the number of algebras of dimension $n$ over GF$(q)$. | ||
| کلیدواژهها | ||
| Enumerating p-groups؛ Enumerating algebras؛ Polynomial On Residue Classes | ||
| مراجع | ||
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J. A. Green (1955) The characters of the finite general linear groups Trans. Amer. Math. Soc. 80, 402-447
G. Higman (1960) Enumerating $p$-groups. I: Inequalities Proc. London Math. Soc. (3) 10, 24-30
G. Higman (1960) Enumerating $p$-groups. II: Problems whose solution is PORC Proc. London Math. Soc. (3)} 10, 566-582
I. G. Macdonald (1979) Symmetric functions and {H}all polynomials The Clarendon
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M. F. Newman, E. A. O'Brien, and M. R. Vaughan-Lee (2004) Groups and nilpotent
{Lie} rings whose order is the sixth power of a prime J. Algebra 278, 383-401
H.~P. Petersson and M. Scherer (2004) The number of nonisomorphic two-dimensional algebras over a finite field Results Math. 45, 137-152
M. Vaughan-Lee (2012) Graham {H}igman's {PORC} conjecture Jahres. Dtsch. Math.-Ver. 114, 89-106
M. Vaughan-Lee (2012) On {G}raham {H}igman's famous {PORC} paper Int. J. Group Theory 1 (4), 65-79
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