#### Document Type

Article

#### Publication Date

2008

#### Department

Mathematics

#### Abstract

Let S, be the symmetric group of degree n where n > 5. Given any non-trivial alpha,beta is an element of S-n, we prove that the product alpha(Sn)beta(Sn) of the conjugacy classes alpha(Sn) and beta(Sn) is never a conjugacy class. Furthermore, if n is odd and not a multiple of three, then alpha(Sn)beta(Sn) is the union of at least three distinct conjugacy classes. We also describe the elements alpha,beta is an element of S-n in the case when alpha(Sn)beta(Sn) is the union of exactly two distinct conjugacy classes.

#### Publication Title

Journal of Group Theory

#### Volume

11

#### Issue

3

#### First Page

371

#### Last Page

379

#### Recommended Citation

Adan-Bante, E.,
Verrill, H.
(2008). Symmetric Groups and Conjugacy Classes. *Journal of Group Theory, 11*(3), 371-379.

Available at: https://aquila.usm.edu/fac_pubs/1759

## Comments

DOI: 10.1515/JGT.2008.021