Base (group theory)

In group theory, a branch of abstract algebra, a "base" refers to a particular set of elements that can be used to generate a group or a subgroup. Specifically, when discussing a group \( G \), a set of elements \( \{ g_1, g_2, \ldots, g_n \} \) is often called a base if these elements can be combined (through the group operation) to form every element of \( G \).