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Group of units in a finite ring

✍ Scribed by David Dolz̆an

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
94 KB
Volume
170
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let G be any group with n elements, where n is a power of a prime or any product of prime powers, not divisible by 4. In this paper we ÿnd all nonisomorphic rings with its group of units isomorphic to G and also ÿnd all groups G with n elements which can be groups of units of a ÿnite ring. We say that a group G is indecomposable, if we cannot write G = HK for some proper, nontrivial subgroups H and K. We ÿnd all ÿnite rings with indecomposable, solvable group of units and ÿnd all ÿnite rings with G = 1+J , where J is the Jacobson radical of R. These results are obtained through a study of p-rings and idempotents in rings yielding decompositions of rings and decompositions of groups of units of rings into product of subgroups.

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