#### Date of Award

2000

#### Document Type

Project

#### Degree Name

Master of Arts in Mathematics

#### Department

Mathematics

#### Abstract

A Steiner system T with parameters (5,6,12) is a collection of 6-element sets, called hexads, of a 12-element set [omega], such that any 5 of the 12 elements belong to exactly one hexad. In this project we construct a graph whose vertices are the orbits of S₁₂ on T x T, where T is the set of all Steiner systems S(5,6,12). Two vertices are joined if an orbit is taken into another under the action of a transposition. The number of hexads common to two Steiner systems are also given. We also prove that any two Steiner systems with parameters (5,6,12) can intersect only in 0, 12, 24, 36, or 60 hexads.

#### Recommended Citation

Dillard, Kristin Marie, "Steiner systems of the Mathieu Group M₁₂" (2000). *Theses Digitization Project*. 1587.

http://scholarworks.lib.csusb.edu/etd-project/1587