LetG be a finite group andX a conjugacy class ofG.We denote rank(G : X) to be theminimumnumber of elements ofX generating G. In the present article, we determine the ranks for two sporadic simple groups, namely the O’Nan sporadic simple group O’N and the Lyons sporadic simple group, Ly. Computations were carried with the aid of the computer algebra systemGAP [The GAP Group, GAP—Groups, Algorith...

We confirm a conjecture about the construction of basis elements for the multiple zeta values (MZVs) at weight 27 and weight 28. Both show as expected one element that is twofold extended. This is done with some lengthy computer algebra calculations using TFORM to determine explicit bases for the MZVs at these weights.

The permutation representation theory of groups has been extended, through quasigroups, to one-sided left (or right) quasigroups. The current paper establishes a link with the theory of ordered sets, introducing the concept of a Burnside order that generalizes the poset of conjugacy classes of subgroups of a finite group. Use of the Burnside order leads to a simplification in the proof of key p...

In this paper we present a decomposition technique to systematically formulate the state equations in symbolic normal-form for linear and/or nonlinear time-invariant large-scale analog circuits with excess elements. The decomposition and the aggregation procedures are shown and an illustrative example is given. The computation program allows the formulation of state equations in a symbolic form...

The Rescorla-Wagner model’s asymptotic predictions are influenced by the initial associative strength under some conditions. This is the case for the experimental paradigm called relative validity. It is possible that stimuli used in the experiment have certain initial associative strength reflecting the subjects’ expectancies. Thus researchers must fully understand this influence. In this arti...

We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order 9 or less. Our approach is novel, using computer algebra to break symmetry and constraint satisfaction search to find candidate solutions. We present new results in algebraic combinatorics: up to isomorphism and ant...

In Algorithm ShortProduct (Hanrot and Zimmermann, 2004, pp. 394–395), at the final step, read return ( ( x2 + xmx2+ x2hx2 mod x. In the printed version, the result might have degree n: if n is odd from the term xm(x2), or if n is even from x2h(x2). The proof of Theorem 2 actually only proves that the result of Algorithm ShortProduct is congruent to f g modulo xn , not that it has degree < n. Wi...