What is pendant group?

A pendant group is a type of cyclic group that arises as a subgroup of a finite group. It is defined as a cyclic group that is not contained in any proper subgroup that is also cyclic. In other words, a pendant group is a maximal cyclic subgroup of a finite group.

Pendant groups are important in group theory because they have applications in areas such as number theory, algebraic geometry, and cryptography. They also have interesting structural properties, such as being self-normalizing and containing a unique maximal subgroup.

Some examples of finite groups that have pendant groups include cyclic groups, some abelian groups, and some dihedral groups. However, not all finite groups have pendant groups.

The study of pendant groups is an active area of research in group theory, with many open questions and conjectures still waiting to be proven.