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Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

An extension of a group H by a group N is a group G with a normal subgroup M such that M=N and G/M=H. This information can be encoded into a short exact sequence of groups ...

A set of generators (g_1,...,g_n) is a set of group elements such that possibly repeated application of the generators on themselves and each other is capable of producing ...

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 ...

The upper central series of a group G is the sequence of groups (each term normal in the term following it) 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... that is constructed in the ...

A special case of nim played by the following rules. Given a heap of size n, two players alternately select a heap and divide it into two unequal heaps. A player loses when ...

An H-space, named after Heinz Hopf, and sometimes also called a Hopf space, is a topological space together with a continuous binary operation mu:X×X->X, such that there ...

A graph is said to be H^*-connected if it is either Hamilton-connected or Hamilton-laceable. S. Wagon (pers. comm., May. 20, 2013; Dupuis and Wagon 2014) conjecture that all ...

A two-dimensional generalization of the Haar transform which is used for the compression of astronomical images. The algorithm consists of dividing the 2^N×2^N image into ...

An algorithm for finding integer relations whose running time is bounded by a polynomial in the number of real variables (Ferguson and Bailey 1992). Unfortunately, it is ...