University of London, Birkbeck College
Department:Economics, Mathematics and Statistics
Position:Department Member
Ben started following the journal Journal of Group Theory.
Ben started following the work of Jessica Leech, University of Cambridge, Philosophy.
Ben started following the work of 3 people.
Papers
Some exceptional Beauville structures
submitted to the Mathematische Zeitschrift. Also available on the arxiv.
We first show that every quasisimple sporadic group possesses an unmixed strongly real Beauville structure aside from the Mathieu groups M11 and M23 (and possibly 2B and M). To do this we give the fi rst generic construction of objects of this kind which in princicpal may be adapted to a number of other cases. We go on to show that no almost simple sporadic group possesses a mixed Beauville structure. We then go on to use the exceptional nature of the alternating group A6 to give a strongly real Beauville structure for this group correcting an earlier error of Fuertes
and Gonzalez-Diez. In doing so we complete the classi cation of alternating groups that possess strongly real Beauville structures. We conclude by discussing mixed Beauville structures of the
groups A6 : 2 and A6:2^2.
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DownloadNew Upper Bounds on the Spreads of the Sporadic Simple Groups
To appear in Communications in Algebra. Note that, compared to the version to be published, this version gives better bounds for M23 and the Baby Monster and contains an additional section giving some concluding remarks.
Let G be a group. We say that G has spread r if for any set of distinct nontrivial elements {x1, . . . , xr} ⊂ G there exists an element y ∈ G with the property that <xi, y> = G for every 1 ≤ i ≤ r. Few bounds on the spread of finite simple groups are known. In this paper we present improved upper bounds for the spread of many of the larger sporadic simple groups, in some cases improving on the best known upper bound by several orders of magnitude.
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A Note On Monomial Representations Linear Groups
a slightly old version of a paper recently accepted by `Communications in Algebra'
A matrix is said to be monomial if every row and column has only one non-zero entry. Let G be a group. A representation \rho: G \rightarrow GL_n(C) is said to be a monomial representation of G if there exists a basis with respect to which \rho(g) is a monomial matrixfor every g\in G. We use elementary methods to classify the irreducible monomial representations of the groups L_2(q), L_3(q) and their natural decorations.
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