Families of Groups

• The trivial group is the group that contains only the identity element. This is denoted .
• The Klein-4 Group, denoted is a group defined by the following table

		a	b	c

• The General Linear Group is the group of invertible matrices under Matrix Multiplication. It is denoted as .

• The Special Linear Group is the group of matrices whose Determinant is . It is denoted as .

• Abelian Group

• Cyclic Group

• The Dihedral Group of order is the group of symmetries of a regular -gon which includes rotations and reflections. It consists to two generators and which correspond to rotation and reflection . It is denoted as .

• Symmetric Group

• Alternating Group

Links §

• Permutations and Orbits
• Fundamental Constructs of Group Theory
• A First Course in Abstract Algebra 7th Edition by Fraleigh