An algebraic characterization of groups with soluble word problem
An algebraic characterization of groups with soluble word problem
复制标题
具有可解应用问题的群的代数表征
DOI：
10.1017/s1446788700019108
复制
发表时间：
1974
影响因子：
0.7
通讯作者：
G. Higman
中科院分区：
文献类型：
--
作者：
W. W. Boone;G. Higman
下面的定理是本文的重点。它规定了一个代数条件，在任何有限生成群中，等价于字问题的溶解度。定理一有限生成群G有可解字问题的充分必要条件是存在一个简单群H和一个有限呈现群K，使得G是H的子群，H是K的子群。
The following theorem is the focal point of the present paper. It stipulates an algebraic condition equivalent, in any finitely generated group, to the solubility of the word problem. THEOREM I. A necessary and sufficient condition that a finitely generated group G have a soluble word problem is that there exist a simple group H, and a finitely presented group K, such that G is a subgroup of H, and H is a subgroup of K.