Application of character estimates to the number of 𝑇2-systems of the alternating group-Reference-Cited by-同舟云学术

Application of character estimates to the number of 𝑇2-systems of the alternating group

Published:2019-05-07 Issue:5 Volume:22 Page:845-864
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Virchow Stefan-C.¹

Affiliation:

1. Institut für Mathematik , Universität Rostock , Ulmenstr. 69 Haus 3, 18057 Rostock , Germany

Abstract

Abstract We use character theory and character estimates to show that the number of T 2

{T_{2}}

-systems of the alternating group A n

{A_{n}}

is at least

1 8 ⁢ n ⁢ 3 ⁢ exp ⁡ ( 2 ⁢ π 6 ⁢ n 1 / 2 ) ⁢ ( 1 + o ⁢ ( 1 ) ) .

\frac{1}{8n\sqrt{3}}\exp\biggl{(}\frac{2\pi}{\sqrt{6}}n^{1/2}\biggr{)}(1+o(1)).

Applying this result, we obtain a lower bound for the number of connected components of the product replacement graph Γ 2 ⁢ ( A n )

{\Gamma_{2}(A_{n})}

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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