A subgroup is a subset of a group that is itself a group under the same operation. This means that the subgroup contains the identity element, is closed under the group operation, and every element has an inverse within the subgroup. Understanding subgroups is crucial in additive combinatorics as they help analyze how structures behave under addition and multiplication, particularly in relation to incidence geometry and solving problems like the sum-product problem.
congrats on reading the definition of subgroup. now let's actually learn it.