Introduction In this talk all groups are finite (by definition), and all simple groups are non-abelian. Let us first define our terms: an involution in a group G is an element t of order 2, i.e. t = 1 and t 6= 1. Its centralizer CG(t) is the subgroup of elements which commute with it, so CG(t) = {g ∈ G | tg = gt}. It has long been accepted in abstract group theory that the way to study simple g...

We introduce a two generated weakly branch contracting automaton group $G$ which is generated by a two state automaton on a three letter alphabet. Using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. Furthermore some algebraic properties of $G$ are detected .

It has long been an open problem whether or not there exists a partial geometry with parameters (s, t, α) = (4, 27, 2). Such a partial geometry, which we call a McLaughlin geometry, would have the McLaughlin graph as point graph. In this note we use tools from computational group theory and computational graph theory to show that a McLaughlin geometry cannot have certain automorphisms, nor can ...

This workshop paper describes automated assessment of CSCL groups based on activity theory. In contrast to our prior work, the algorithms and analysis presented here focus entirely at the small group unit of analysis. The work presented is exploratory and preliminary in nature. It is our hope to refine it through participation in this workshop.

For many decision problems on a finitely presented group G, we can quickly weed out negative solutions by using much quicker algorithms on an appropriately chosen quotient group G/K of G. However, the behavior of such “quotient tests” can be sometimes paradoxical. In this paper, we analyze a few simple case studies of quotient tests for the classical identity, word, conjugacy problems in groups...

We present an automatic technique for the detection of structural symmetry in a model directly from its Promela specification. Our approach involves finding the static channel diagram of the model, a graphical representation of channel-based system communication; computing the group of symmetries of this diagram; and computing the largest possible subgroup of these symmetries which induce autom...

It is known that any chordal graph can be uniquely decomposed into simplicial components. Based on this fact, it is shown that for a given chordal graph, its automorphism group can be computed in O((c! · n)O(1)) time, where c denotes the maximum size of simplicial components and n denotes the number of nodes. It is also shown that isomorphism of those chordal graphs can be decided within the sa...

thirty nine novel 1,2,3,4-tetrahydropyrimidinone (thione)s were subjected to conformational studies. density functional theory at b3lyp/6-31 g* was performed as the computational method of high accuracy. important dihedral angles and bond lengths were investigated and the values obtained were explainable. results of this work confirm a twisted boat tetrahydropyrimidine ring conformation with an...