Application of Character Estimates to the Number of $T_2$-Systems of the Alternating Group

DOI10.1515/JGTH-2019-2049arXiv1710.10063MaRDI QIDQ6293118

Publication date: 27 October 2017

Abstract: We use character theory and character estimates to show that the number of

T_{2}

-systems of

A_{n}

is at least �egin{equation*} frac{1}{8nsqrt{3}}expleft(frac{2pi}{sqrt{6}}n^{1/2} ight)(1+o(1)). end{equation*} Applying this result, we obtain a lower bound for the number of connected components of the product replacement graph

G a m m a_{2} (A_{n})

.

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Simple groups: alternating groups and groups of Lie type (20D06)

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