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Compact rings having a finite simple group of units

✍ Scribed by Jo-Ann Cohen; Kwangil Koh

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
995 KB
Volume
119
Category
Article
ISSN
0022-4049

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✦ Synopsis

For a compact Hausdorff ring, one observes that the group of units is a totally disconnected compact topological group and is a finite simple group if and only if it possesses no nontrivial closed normal subgroups. Three classification theorems for compact rings are now given. First, those compact rings with identity having a finite simple group of units are identified. Second, a classification of all compact rings A with identity for which 2 is a unit in A, G modulo the center of G is a finite simple group and the length of W is less than or equal to 4 (or equivalently, W is a torsion group) is given where G is the group of units in A and W is the subgroup of G generated by {SE G: g2 = I}. Finally, those compact rings with identity having 2 as a unit and for which W is a nilpotent group are identified. @

πŸ“œ SIMILAR VOLUMES

Group of units in a finite ring
Group of units in a finite ring
✍ David DolzΜ†an πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 94 KB

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 ΓΏnd all nonisomorphic rings with its group of units isomorphic to G and also ΓΏnd all groups G with n elements which can be groups of units of a ΓΏnite ring. We say th