Center of a Group


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Center of a Group

 

(or central of a group), in mathematics. The center of a group is the set of all elements of the group that commute with every element of the group. In other words, it is the set of elements z such that zg = gz for every element g of the given group G. The center is a subgroup of G. It is transformed into itself under all automorphisms of G (seeISOMORPHISM). The center of the group of nonsingular matrices of order n is the subgroup of scalar matrices, that is, matrices of the form λE, where λ is a number and E is the identity matrix.

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Eager inquiries concerning the twins were pouring into their enchanted ears all the time; each was the constant center of a group of breathless listeners; each recognized that she knew now for the first time the real meaning of that great word Glory, and perceived the stupendous value of it, and understand why men in all ages had been willing to throw away meaner happiness, treasure, life itself, to get a taste of its sublime and supreme joy.
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