“School of Mathematics”
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| Paper IPM / M / 502 |
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| Abstract: | |||||||||
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Recently, it has been shown that if D is a finite dimensional
division ring then GLn(D) is not finitely generated [2]. Our
object here is to provide a general framework for the groups of
units of the left artinian rings. We prove that if R is an
infinite F-algebra of finite dimension over F, then U(R) is
not finitely generated. We show that none of infinite subnormal
subgroups of GLn(D) has finite maximal subgroup. Also in this
article, we prove that for any infinite left artinian ring R,
U(R) has no finite maximal subgroup, a result is analogous to
one for rings [6].
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