Duyan, Hülya and Halasi, Zoltán and Podoski, Károly (2019) Random bases for coprime linear groups. JOURNAL OF GROUP THEORY. ISSN 1433-5883 (In Press)
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Abstract
The minimal base size b(G) for a permutation group G is a widely studied topic in permutation group theory. Z. Halasi and K. Podoski proved that b(G) is at most 2 for coprime linear groups. Motivated by this result and the probabilistic method used by T. Burness, M. W. Liebeck and A. Shalev, it was asked by L. Pyber whether or not, for coprime linear groups there exists a constant c such that the probability that a random c-tuple is a base for G tends to 1 as |V| tends to infinity. While the answer to this question is negative in general, it is positive under the additional assumption that G is primitive as a linear group. In this paper, we show that almost all 11-tuples are bases for coprime primitive linear groups.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra |
| Depositing User: | Zoltán Halasi |
| Date Deposited: | 13 Sep 2019 07:06 |
| Last Modified: | 06 Apr 2023 07:21 |
| URI: | http://real.mtak.hu/id/eprint/99263 |
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