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The minimal generating sets of $\mathrm{PSL} (2, p)$ of size four

Published online by Cambridge University Press:  06 November 2013

Sebastian Jambor*
Affiliation:
Department of Mathematics The University of Auckland Private Bag 92019 Auckland, New Zealand email [email protected]

Abstract

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We show that there are only finitely many primes $p$ such that $\mathrm{PSL} (2, p)$ has a minimal generating set of size four.

Supplementary materials are available with this article.

Type
Research Article
Copyright
© The Author(s) 2013 

References

Atiyah, M. F. and Macdonald, I. G., Introduction to commutative algebra (Addison-Wesley, Reading, MA, 1969).Google Scholar
Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system. I. The user language’, J. Symbolic Comput. 24 (1997) 235265; Computational algebra and number theory (London, 1993).CrossRefGoogle Scholar
Donkin, S., ‘Invariants of several matrices’, Invent. Math. 110 (1992) 389401.CrossRefGoogle Scholar
Drensky, V., ‘Defining relations for the algebra of invariants of $2\times 2$ matrices’, Algebr. Represent. Theory 6 (2003) 193214.CrossRefGoogle Scholar
The GAP group, ‘GAP – groups, algorithms, and programming, Version 4.4.12’, 2008.Google Scholar
Horowitz, R. D., ‘Characters of free groups represented in the two-dimensional special linear group’, Comm. Pure Appl. Math. 25 (1972) 635649.CrossRefGoogle Scholar
Jambor, S., ‘Computing minimal associated primes in polynomial rings over the integers’, J. Symbolic Comput. 46 (2011) 10981104.CrossRefGoogle Scholar
Jambor, S., ‘An  ${\mathrm{L} }_{3} {{\unicode{x2013}}}{\mathrm{U} }_{3} $ -quotient algorithm for finitely presented groups’, PhD Thesis, RWTH Aachen University, 2012.Google Scholar
Nachman, B., ‘Generating sequences of $\mathrm{PSL} (2, p)$ ’, Preprint, 2012, arXiv:1210.2073 [math.GR].Google Scholar
Plesken, W. and Fabiańska, A., ‘An ${L}_{2} $ -quotient algorithm for finitely presented groups’, J. Algebra 322 (2009) 914935.CrossRefGoogle Scholar
Procesi, C., ‘The invariant theory of $n\times n$ matrices’, Adv. Math. 19 (1976) 306381.CrossRefGoogle Scholar
Whiston, J. and Saxl, J., ‘On the maximal size of independent generating sets of ${\mathrm{PSL} }_{2} (q)$ ’, J. Algebra 258 (2002) 651657.CrossRefGoogle Scholar
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