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For a subgroup H of a group G and an element x of G, define xH to be the set {xh:h in H} and Hx to be the set {hx:h in H}. A subset of G of the form xH for some x in G is ...

A module over a unit ring R is called divisible if, for all r in R which are not zero divisors, every element m of M can be "divided" by r, in the sense that there is an ...

A group action G×X->X is effective if there are no trivial actions. In particular, this means that there is no element of the group (besides the identity element) which does ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

A minimal free resolution of a finitely generated graded module M over a commutative Noetherian Z-graded ring R in which all maps are homogeneous module homomorphisms, i.e., ...

A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f(g_1g_2)=f(g_1)f(g_2) for all g_1,g_2 in G, where the product on the ...

An n-Hadamard graph is a graph on 4n vertices defined in terms of a Hadamard matrix H_n=(h)_(ij) as follows. Define 4n symbols r_i^+, r_i^-, c_i^+, and c_i^-, where r stands ...

In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...