A subgroup of direct product is a subset of the direct product of two or more groups that is itself a group under the same operation.
A subgroup of direct product is a subgroup of the direct product of two or more groups, while a subgroup of a single group is a subgroup of a single group under the same operation. In other words, a subgroup of direct product contains elements from multiple groups, while a subgroup of a single group contains elements from only one group.
Studying subgroups of direct product allows us to understand the relationships and structures between multiple groups. It also helps us to identify common properties and characteristics among different groups.
A subgroup of direct product can be isomorphic to another subgroup of direct product if they have the same structure and are related by a group isomorphism. This means that they have the same number of elements and the same operation, but the elements may be arranged differently.
Yes, a subgroup of direct product can be isomorphic to one of its parent groups if it contains all the elements of that parent group. However, this is not always the case as a subgroup of direct product can also have elements from other parent groups.