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2019 On the covering number of $S_{14}$
Ryan Oppenheim, Eric Swartz
Involve 12(1): 89-96 (2019). DOI: 10.2140/involve.2019.12.89

Abstract

If all elements of a group G are contained in the set-theoretic union of proper subgroups H 1 , , H n , then we define this collection to be a cover of G . When such a cover exists, the cardinality of the smallest possible cover is called the covering number of G , denoted by σ ( G ) . Maróti determined σ ( S n ) for odd n 9 and provided an estimate for even n . The second author later determined σ ( S n ) for n 0 ( mod 6 ) when n 1 8 , while joint work of the second author with Kappe and Nikolova-Popova also verified that Maróti’s rule holds for n = 9 and established the covering numbers of S n for various other small n . Currently, n = 1 4 is the smallest value for which σ ( S n ) is unknown. In this paper, we prove the covering number of S 1 4 is 3 0 9 6 .

Citation

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Ryan Oppenheim. Eric Swartz. "On the covering number of $S_{14}$." Involve 12 (1) 89 - 96, 2019. https://doi.org/10.2140/involve.2019.12.89

Information

Received: 9 July 2017; Revised: 28 November 2017; Accepted: 30 December 2017; Published: 2019
First available in Project Euclid: 26 October 2018

zbMATH: 06887333
MathSciNet: MR3810480
Digital Object Identifier: 10.2140/involve.2019.12.89

Subjects:
Primary: 20-04, 20D60

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2019
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