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The Poincaré group is another name for the inhomogeneous Lorentz group (Weinberg 1972, p. 28) and corresponds to the group of inhomogeneous Lorentz transformations, also ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

The monster group is the highest order sporadic group M. It has group order |M| = (1) = (2) where the divisors are precisely the 15 supersingular primes (Ogg 1980). The ...

Rubik's group is the group corresponding to possible rotations of a Rubik's Cube. There are six possible rotations, each corresponding to a generator of the group, and the ...

The trivial group, denoted E or <e>, sometimes also called the identity group, is the unique (up to isomorphism) group containing exactly one element e, the identity element. ...

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...

The group of functions from an object G to itself which preserve the structure of the object, denoted Aut(G). The automorphism group of a group preserves the multiplication ...

The Heisenberg group H^n in n complex variables is the group of all (z,t) with z in C^n and t in R having multiplication (w,t)(z,t^')=(w+z,t+t^'+I[w^*z]) (1) where w^* is the ...