Final answer:
To find a group G with a subgroup H having a finite number of right cosets modulo H, we can consider the group of integers ℤ with the subgroup of multiples of an integer n, as this subgroup has n distinct right cosets.
Step-by-step explanation:
The question is asking us to find a group G that contains a subgroup H for which there are a finite number of right cosets of H in G. A well-known example of such a group G would be the group of integers under addition, ℤ, with H being the subgroup of multiples of some integer n, for example nℤ where n > 0. This subgroup H has exactly n right cosets, namely the sets of integers congruent to each of the numbers 0, 1, ..., n-1 modulus n. These cosets are typically denoted as 0 + H, 1 + H, ..., (n-1) + H.
Right cosets are a fundamental concept in the field of group theory, which is a part of abstract algebra. They are important in many areas of mathematics, including number theory and the study of symmetry in objects.