Halasi, Zoltán and Liebeck, M.W. and Maróti, Attila (2019) Base sizes of primitive groups: bounds with explicit constants. JOURNAL OF ALGEBRA, 521. pp. 16-43. ISSN 0021-8693
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Abstract
We show that the minimal base size $b(G)$ of a finite primitive permutation group $G$ of degree $n$ is at most $2 (\log |G|/\log n) + 24$. This bound is asymptotically best possible since there exists a sequence of primitive permutation groups $G$ of degrees $n$ such that $b(G) = \lfloor 2 (\log |G|/\log n) \rceil - 2$ and $b(G)$ is unbounded. As a corollary we show that a primitive permutation group of degree $n$ that does not contain the alternating group $\mathrm{Alt}(n)$ has a base of size at most $\max\{\sqrt{n} , \ 25\}$.
Item Type: | Article |
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Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra |
Depositing User: | dr. Attila Maroti |
Date Deposited: | 13 Sep 2019 09:10 |
Last Modified: | 13 Sep 2019 09:10 |
URI: | http://real.mtak.hu/id/eprint/99291 |
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