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Papers by Edmund Robertson

The Atlas of Finite Groups - Ten Years On

In this paper we examine series of finite presentations which are invariant under the full symmet... more In this paper we examine series of finite presentations which are invariant under the full symmetric group acting on the set of generators. Evidence from computational experiments reveals a remarkable tendency for the groups in these series to be closely related to the orthogonal groups. We examine cases of finite groups in such series and look in detail at an infinite group with such a presentation. We prove some theoretical results about 3-generator symmetric presentations and make a number of conjectures regarding n-generator symmetric presentations.

'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this... more 'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this second volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by John Meakin (Lincoln, Nebraska) and Ákos Seress (Ohio State). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.

Algebra Through Practice, 1985

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1986

SynopsisIn this paper we give two generator, two relation presentations for the following perfect... more SynopsisIn this paper we give two generator, two relation presentations for the following perfect groups which were not previously known to have deficiency zero: SL(2, 32), SL(2, 64), SL(2, 27), SL(2, 49), Â7, Ŝz(8), SL(2, 5) × SL(2, 5), SL(2, 5) × SL(2, 25). We also give two generator, two relation presentations for three other finite perfect groups, two having SL(2, 7) as an image and one having SL(2, 5) as an image. We also discuss presentations for certain other perfect groups which were known to have deficiency zero and find some neat new presentations for them.

Semigroup Forum, 1993

... RESEARCH ARTICLE On a class of semigroups with symmetric presentations CM Campbell, EF Robert... more ... RESEARCH ARTICLE On a class of semigroups with symmetric presentations CM Campbell, EF Robertson and RM Thomas Communicated by JM Howie ... go = 2,gl = 1, and g~ = g,,-1 +g~-2 for n > 2. Page 2. CAMPBELL, ROBERTSON AND THOMAS ...

ACM SIGSAM Bulletin, 1991

Preface Background reference material 1. Sets 2. Relations 3. Mappings Solutions to chapter 1 Sol... more Preface Background reference material 1. Sets 2. Relations 3. Mappings Solutions to chapter 1 Solutions to chapter 2 Solutions to chapter 3 Test paper 1 Test paper 2 Test paper 3 Test paper 4.

In this chapter we shall apply some of the previous results in a study of certain types of linear... more In this chapter we shall apply some of the previous results in a study of certain types of linear forms.

In Theorem 2.6 we obtained, for an inner product space V and a finite-dimensional subspace W of V... more In Theorem 2.6 we obtained, for an inner product space V and a finite-dimensional subspace W of V, a direct sum decomposition of the form V = W ⊕W⊥. We now consider the following general notion.

Canadian Mathematical Bulletin, 1975

Let Fn be the free group on {ai:i ∊ ℤ n} where the set of congruence classes mod n is used as an ... more Let Fn be the free group on {ai:i ∊ ℤ n} where the set of congruence classes mod n is used as an index set for the generators. The permutation (1, 2, 3, …, n) of ℤn induces an automorphism θ of Fn by permuting the subscripts of the generators. Suppose w is a word in Fn and let N(w) denote the normal closure of {wθi-1:l ≤i≤n}. Define the group Gn(w) by Gn(w)=Fn/N(w) and call wdi-1=l the relation (i) of Gn(w).

Bulletin of the London Mathematical Society, 2012

Journal of the Australian Mathematical Society, 2000

It is known that the direct product of two automatic groups is automatic. The notion of automatic... more It is known that the direct product of two automatic groups is automatic. The notion of automaticity bas been extended to semigroups, and this for groups has been generalized to automatic monoids. However, the direct product of two automatic semigroups need not be finitely generated and hence not automatic.Robertson, Ruškuc and Wiegold have determined necessary and sufficient conditions for the direct product of two finitely generated semigroups to be finitely generated. Building on this, we prove the following. Let S and T be automatic semigroups; if S and T are infinite, then S × T is automatic if and only if S2 = S and T2 = T; if S is finite and T is infinite, then S × T is automatic if and only if S2 = S. As a consequence, we have that, if S and T are automatic semigroups, then S × T is automatic if and only if S × T is finitely generated.

Bulletin of the London Mathematical Society, 1974

Applications of Fibonacci Numbers, 2004

For a finitely generated group G = A , where A = {a 1 , a 2 ,. .. , a n }, the sequence x i = a i... more For a finitely generated group G = A , where A = {a 1 , a 2 ,. .. , a n }, the sequence x i = a i , 1 ≤ i ≤ n, x i+n = n j=1 x i+j−1 , i ≥ 1, is called the Fibonacci orbit of G with respect to the generating set A, denoted F A (G). If F A (G) is periodic we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LEN A (G). In this paper we examine the Fibonacci lengths of D i 2m , i > 1 where D 2m is the dihedral group of order 2m.