subsubgroup

A subsubgroup, also known as a subgroup of a subgroup, is a concept in group theory, a branch of abstract algebra. In group theory, a group is a set equipped with a binary operation that satisfies certain properties, including closure, associativity, identity, and invertibility. A subgroup is a subset of a group that itself forms a group under the same operation.

A subsubgroup is a subgroup of a subgroup. To be more precise, if G is a group and H is a subgroup of G, then a subsubgroup of G is a subgroup of H. This concept is useful in various areas of mathematics and its applications, such as in the study of symmetries, permutations, and transformations.

The concept of subsubgroups can be extended to higher levels. For example, a subgroup of a subsubgroup is called a subsubsubgroup, and so on. However, in practice, the term "subsubgroup" is typically used to refer to subgroups of subgroups, and not further nested subgroups.

In summary, a subsubgroup is a subgroup of a subgroup in group theory. This concept is fundamental in understanding the structure and properties of groups and their subgroups.