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S are called generators of G, if every element of G can be expressed as a finite product of their powers.
Advanced Parallel Processing Technologies: 7th International Symposium, APPT ... - 242. lappuse
laboja - 2007 - 772 lapas
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## Point Group Character Tables and Related Data

J. A. Salthouse, M. J. Ware, Salthouse - 1972 - 88 lapas
...nuclei to which they may be spin coupled. A set, P, of elements of a finite group, G, is a system of generators of G, if every element of G can be expressed as a product containing only integer powers (positive or negative) of elements of P. The elements of P are...
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## Linear Algebra: A Geometric Approach

E. Sernesi - 1993 - 384 lapas
...to which Z/nZ is an abelian group. 14.12 Let G be a group. A subset G of G is said to be a system of generators of G if every element of G can be expressed as a product of a finite number of elements of G and their inverses. If (7 is a finite set then G is said...
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## Graph Symmetry: Algebraic Methods and Applications

Gena Hahn, Gert Sabidussi - 1997 - 418 lapas
...elements of a subset 5 of a group G are called generators of G, and S is said to be a generating set, if every element of G can be expressed as a finite product of their powers. We will also say that G is generated by S. We will denote by Gr(5)' the subgroup of a group G generated...
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## Group Theory with Applications in Chemical Physics

Patrick Jacobs - 2005
...group of order /;, when binary composition is defined to be the multiplication of complex numbers. If every element of G can be expressed as a finite product of powers of the elements in a particular subset of G, then the elements of this subset are called the...
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## The Topology of the 2x2 Games: A New Periodic Table

David Robinson, David Goforth - 2005 - 179 lapas
...rational choice. Generators, Set of A set of elements of a discrete group G with the property that every element of G can be expressed as a finite product of powers of the members of the set. Graph A set of nodes, or vertices, and the set of edges that connect...
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## Canadian Journal of Mathematics - 1964

Žurnāls - 16. sēj.,Nr. 3 - 208 lapas
...gi, g 2 ,    , f«. Suppose that gi, g 2 , . . . , gi, form a minimal set of generators, ie, every element of G can be expressed as a finite product of powers of these h elements and no Received August 12, 1963. Research supported by a Postdoctorate Fellowship...