Fuchs' problem for dihedral groups

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• 作者：Sunil K. Chebolu^a ; ^{schebol@ilstu.edu} ; Keir Lockridge^b ; ^{klockrid@gettysburg.edu}
• 关键词：Primary ; 11T06 ; 20K10 ; secondary ; 06F20
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：221
• 期：4
• 页码：971-982
• 全文大小：348 K
• 卷排序：221

文摘

More than 50 years ago, László Fuchs asked which abelian groups can be the group of units of a ring. Though progress has been made, the question remains open. One could equally well pose the question for various classes of nonabelian groups. In this paper, we prove that D2,D4,D6,D8D2,D4,D6,D8, and D12D12 are the only dihedral groups that appear as the group of units of a ring of positive characteristic (or, equivalently, of a finite ring), and D2D2 and D4kD4k, where k is odd, are the only dihedral groups that appear as the group of units of a ring of characteristic 0.