Abstract For all sufficiently large odd integers n, the following version of Higman's embedding theorem is proved in the variety B n of all groups satisfying the identity x n = 1 . A finitely generated group G from B n has a presentation G = 〈 A | R 〉 with a finite set of generators A and a recursively enumerable set R of defining relations if and only if it is a subgroup of a group H finitely presented in the variety B n . It follows that there is a ‘universal’ 2-generated finitely presented in B n group containing isomorphic copies of all finitely presented in B n groups as subgroups.

中文翻译：

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在 Burnside 变种中有限地呈现的群

摘要 对于所有足够大的奇数 n，以下版本的 Higman 嵌入定理在满足恒等式 xn = 1 的所有群的变体 B n 中得到证明。从 B n 有限生成的群 G 有一个表示 G = < A | R 〉 具有有限的生成元集 A 和定义关系的递归可枚举集 R 当且仅当它是有限地呈现在变体 B n 中的群 H 的子群。因此，在 B n 群中存在一个“普遍的”2-生成的有限表示，它包含作为子群在 B n 群中所有有限表示的同构副本。