Article contents
The minimal generating sets of $\mathrm{PSL} (2, p)$ of size four
Part of:
Linear algebraic groups and related topics
Structure and classification of infinite or finite groups
Published online by Cambridge University Press: 06 November 2013
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We show that there are only finitely many primes $p$ such that $\mathrm{PSL} (2, p)$ has a minimal generating set of size four.
MSC classification
- Type
- Research Article
- Information
- 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) 235–265; Computational algebra and number theory (London, 1993).CrossRefGoogle Scholar
Donkin, S., ‘Invariants of several matrices’, Invent. Math.
110 (1992) 389–401.CrossRefGoogle Scholar
Drensky, V., ‘Defining relations for the algebra of invariants of
$2\times 2$
matrices’, Algebr. Represent. Theory
6 (2003) 193–214.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) 635–649.CrossRefGoogle Scholar
Jambor, S., ‘Computing minimal associated primes in polynomial rings over the integers’, J. Symbolic Comput.
46 (2011) 1098–1104.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) 914–935.CrossRefGoogle Scholar
Procesi, C., ‘The invariant theory of
$n\times n$
matrices’, Adv. Math.
19 (1976) 306–381.CrossRefGoogle Scholar
Whiston, J. and Saxl, J., ‘On the maximal size of independent generating sets of
${\mathrm{PSL} }_{2} (q)$
’, J. Algebra
258 (2002) 651–657.CrossRefGoogle Scholar
You have
Access
- 5
- Cited by