In this paper, considering the concept of Universal Multiplication Table, we show that for every n ≥ 2, the inequality: M(n) = #{ij|1 ≤ i, j ≤ n} ≥ n2 N(n2) , holds true with: N(n) = n log 2 log log n ( 1+ 387 200 log log n )

The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational charact...

Unlike those used in the West, a typical Chinese multiplication table includes only smaller-operand-first entries (e.g., 3 x 7=21, but not 7 x 3=21). Due to this unique feature, multiplication for Chinese subjects has been found to show an operand-order effect. The present study aims to investigate the neural bases of the operand-order effect. Subjects were 20 Mainland Chinese subjects who lear...

The Cayley Group Membership problem (CGM) is to input a groupoid (binary algebra) G given as a multiplication table, a subset X of G, and an element t of G, and to determine whether t can be expressed as a product of elements of X. For general groupoids CGM is P-complete, and for associative algebras (semigroups) it is NL-complete. Here we investigate CGM for particular classes of groups. The p...

We use presentations and identities among relations to give a generalisation of the Schreier theory of nonabelian extensions of groups. This replaces the usual multiplication table for the extension group by more efficient, and often geometric, data. The methods utilise crossed modules and crossed resolutions.

We give a polynomial time algorithm that computes a decomposition of a finite group G given in the form of its multiplication table. That is, given G, the algorithm outputs two subgroups A and B of G such that G is the direct product of A and B, if such a decomposition exists.

By using functional magnetic resonance imaging (fMRI), the neural substrates involved in mental recitation of the single-digit multiplication table and serial subtraction were studied. The former depends mostly on well-learned arithmetical facts, while the latter requires arithmetic processing. Activation during each task was compared with that in a number counting control. During the recitatio...

‎the purpose of this paper is the determination of the inertia‎ ‎factors‎, ‎the computations of the fischer matrices and the ordinary‎ ‎character table of the split extension $overline{g}=‎ ‎3^{7}{:}sp(6,2)$ by means of clifford-fischer theory‎. ‎we firstly‎‎determine the conjugacy classes of $overline{g}$ using the coset‎ ‎analysis method‎. ‎the determination of the inertia factor groups of‎ ‎...

in this paper we give some general results on the non-splitextension group $overline{g}_{n} = 2^{2n}{^{cdot}}sp(2n,2), ngeq2.$ we then focus on the group $overline{g}_{4} =2^{8}{^{cdot}}sp(8,2).$ we construct $overline{g}_{4}$ as apermutation group acting on 512 points. the conjugacy classes aredetermined using the coset analysis technique. then we determine theinertia factor groups and fischer...