Abstract
Let R be a local ring, with maximal ideal m , and residue class division ring R/ m = D. Denote by R* = G L 1(R), the group of units of R. Here we investigate some algebraic structure of subnormal and maximal subgroups of R*. For instance, when D is of finite dimension over its center, it is shown that finitely generated subnormal subgroups of R* are central. It is also proved that maximal subgroups of R* are not finitely generated. Furthermore, assume that P is a nonabelian maximal subgroup of R* such that P contains a noncentral soluble normal subgroup of finite index, it is shown that D is a crossed product division algebra.
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Acknowledgments
The second author is indebted to the Research Council of Sharif University of Technology and the Abdus Salam International Centre for Theoretical Physics for support.
Notes
#Communicated by C. Pedrini.