The subgroup of a specified group generated by the larger group's commutators.

plural of derived group

(group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition.

Any of several small groups of people, at a conference etc., who concentrate effort on a part of the main topic.

(in an experiment) The group of test subjects left untreated or unexposed to some procedure and then compared with treated subjects in order to validate the results of the test.

plural of abelian group

(algebra) Given ring R with identity not equal to zero, and group G=g_1,g_2,...,g_n, the group ring RG has elements of the form a_1g_1+a_2g_2+...+a_ng_n (where a_i isin R) such that the sum of a_1g_1+a_2g_2+...+a_ng_n and b_1g_1+b_2g_2+...+b_ng_n is (a_1+b_1)g_1+(a_2+b_2)g_2+...+(a_n+b_n)g_n and the product is ∑ₖ₌₁ⁿ(∑_(g_ig_j=g_k)a_ib_j)g_k.

(sports) the stage of a competition where teams in the same group play each other, usually before the knockout stage.

plural of steering group

A committee whose function is to arrange the schedules of business for a legislative assembly or other organization