###
*Irish* *Math*. Soc. Bulletin 59 (2007), 9–27 9

"... Following an illness that lasted for about one year, Gerard Mur- ..."

###
*Irish* *Math*. Soc. Bulletin 56 (2005), 103–113 103 Groups with Few Normalizer Subgroups

"... Abstract. The behaviour of normalizer subgroups of a group has often a strong influence on the structure of the group it-self. In this paper groups with finitely many normalizers of subgroups with a given property χ are investigated, for vari-ous relevant choices of the property χ. 1. ..."

Abstract
- Add to MetaCart

Abstract. The behaviour of normalizer subgroups of a group has often a strong influence on the structure of the group it-self. In this paper groups with finitely many normalizers of subgroups with a given property χ are investigated, for vari-ous relevant choices of the property χ. 1.

###
*Irish* *Math*. Soc. Bulletin 56 (2005), 37–51 37 Locally Nilpotent Linear Groups

"... Abstract. This article examines aspects of the theory of locally nilpotent linear groups. We also present a new classification result for locally nilpotent linear groups over an arbitrary field F. 1. Why Locally Nilpotent Linear Groups? Linear (matrix) groups are a commonly used concrete representat ..."

Abstract
- Add to MetaCart

Abstract. This article examines aspects of the theory of locally nilpotent linear groups. We also present a new classification result for locally nilpotent linear groups over an arbitrary field F. 1. Why Locally Nilpotent Linear Groups? Linear (matrix) groups are a commonly used concrete representation of groups. The first investigations of linear groups were undertaken in the second half of the 19th century, and currently linear group theory is a highly developed branch of group theory. In the past few decades interest in matrix groups has revived and increased, driven partly by the rapid development of computational group theory. Locally nilpotent groups are a generalization of nilpotent groups. Over the years, many structural and classification results for locally nilpotent linear groups have been obtained. Further progress in the study of these groups is possible using computational techniques. Group theoretical algorithms take as input a finite generating set for a group. The celebrated ‘Tits alternative ’ states that a finitely generated linear group G either is solvable-by-finite (that is, G contains a normal solvable subgroup of finite index), or G contains a nonabelian free subgroup. For linear groups of the latter type, some basic computational problems, such as membership testing and the conjugacy problem, are undecidable in general. Nilpotent linear groups on the other hand are solvable-by-finite and so are more suitable for computation (note that the class of nilpotent-by-finite linear

###
*Irish* *Math*. Soc. Bulletin 62 (2008), 71–78 71 Minimizing Oblique Errors for Robust Estimating

"... Abstract. The slope of the best fit line from minimizing the sum of the squared oblique errors is shown to be the root of a polynomial of degree four. We introduce a median estimator for the slope and, using a case study, we show that the median estimator is robust. 1. ..."

Abstract
- Add to MetaCart

Abstract. The slope of the best fit line from minimizing the sum of the squared oblique errors is shown to be the root of a polynomial of degree four. We introduce a median estimator for the slope and, using a case study, we show that the median estimator is robust. 1.

###
*Irish* *Math*. Soc. Bulletin 59 (2007), 65–70 65 Convergence from Below Suffices

"... Abstract. An elementary application of Fatou’s lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in any introductory course on measure and integration ..."

Abstract
- Add to MetaCart

Abstract. An elementary application of Fatou’s lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in any introductory course on measure and integration. 1. The Convergence from Below Theorem Three famous convergence-related results appear in most introduc-tory courses on measure and integration: the monotone convergence theorem, Fatou’s lemma and the dominated convergence theorem. In teaching this material it is common to follow the approach taken in, for example, [1, Chapter 1]. There Rudin begins by proving the monotone convergence theorem and then deduces Fatou’s lemma. Finally, he deduces the dominated convergence theorem from Fa-tou’s lemma. The result which we call the convergence from below

###
*Irish* *Math*. Soc. Bulletin 47 (2001), 27–39 27 Representations and Derivations of Modules

"... Abstract. In this article we define and study derivations between bimodules. In particular, we define the Gelfand radical of a Banach bimodule and show that, under some reasonable conditions, every derivation between two Banach bimodules over a commutative Banach algebra maps into the Gelfand radica ..."

Abstract
- Add to MetaCart

Abstract. In this article we define and study derivations between bimodules. In particular, we define the Gelfand radical of a Banach bimodule and show that, under some reasonable conditions, every derivation between two Banach bimodules over a commutative Banach algebra maps into the Gelfand radical. This is a module version of the famous Singer-Wermer Theorem. 1.

###
*Irish* *Math*. Soc. Bulletin 54 (2004), 25–31 25 On Cotorsion Images of the Baer–Specker Group

"... A paper in the Bulletin [1] some years ago has discussed in detail the so-called Baer–Specker group P, the full Cartesian product of count-ably many copies of the integers, Z. Despite its seemingly straight-forward presentation as P = i∈ω Zei = Zω, this group has a very rich structure of subgroups: ..."

Abstract
- Add to MetaCart

A paper in the Bulletin [1] some years ago has discussed in detail the so-called Baer–Specker group P, the full Cartesian product of count-ably many copies of the integers, Z. Despite its seemingly straight-forward presentation as P = i∈ω Zei = Zω, this group has a very rich structure of subgroups: on the one hand it is an ℵ1-free group (i.e., all its countable subgroups are free Abelian groups — see [4, Theorem 19.2]), but on the other hand it also possesses subgroups which exhibit a high degree of pathological behaviour. There is, for example, a subgroup G of P with the property that G ∼ = G⊕G⊕G but G G⊕G — see [2]. The objective of the current paper is to consider the epimorphic images of P and to show that these are classifiable in a very clear way, but that the possible images are very wide-ranging. Before establishing the desired results we recall some standard

###
*Irish* *Math*. Soc. Bulletin 61 (2008), 65–75 65 The Undergraduate Ambassadors Scheme in Ireland

"... Abstract. In this article I will briefly describe the Under-graduate Ambassadors Scheme which has been running in the UK since 2002. This scheme provides university depart-ments with a framework for running a module that awards academic credit to undergraduates for developing transfer-able skills, w ..."

Abstract
- Add to MetaCart

Abstract. In this article I will briefly describe the Under-graduate Ambassadors Scheme which has been running in the UK since 2002. This scheme provides university depart-ments with a framework for running a module that awards academic credit to undergraduates for developing transfer-able skills, while working with teachers in local schools. I will explain why I chose to coordinate an Undergraduate Ambas-sadors Scheme module in mathematics in University College Dublin and discuss what is involved in setting-up, running, and assessing such a module. 1.

###
*Irish* *Math*. Soc. Bulletin 64 (2009), 31–42 31 A little Help from my Friends

"... This is a tribute to my dear colleagues and friends David Walsh and Richard Watson, who were here before me in Maynooth, and who laboured with me in the day and the heat. They cheerfully shouldered with me a teaching load that would, apparently, kill the ..."

Abstract
- Add to MetaCart

This is a tribute to my dear colleagues and friends David Walsh and Richard Watson, who were here before me in Maynooth, and who laboured with me in the day and the heat. They cheerfully shouldered with me a teaching load that would, apparently, kill the

###
*Irish* *Math*. Soc. Bulletin 56 (2005), 81–85 81 Fibonacci Sequences in Groups

"... An ordered pair (x1, x2) of elements of a group G determines a se-quence in G by the rule xnxn+1 = xn+2, n ∈ N. (1) When this sequence is periodic, its fundamental period is called the ..."

Abstract
- Add to MetaCart

An ordered pair (x1, x2) of elements of a group G determines a se-quence in G by the rule xnxn+1 = xn+2, n ∈ N. (1) When this sequence is periodic, its fundamental period is called the