Scholarlink

Abstract <p> While MacLane’s version of the Kurosh subgroup theorem for free products has been well-known, one of its implications seems to have escaped the attention of the mathematical community. The purpose of this note is to fill this gap by providing this implication. It asserts that a nontrivial normal subgroup of a group is a free factor of this subgroup’s normal closure in the free product of the group with arbitrary nontrivial groups. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An Implication of the Kurosh–MacLane Subgroup Theorem for Free Products

  • 期刊论文

  • 发表日期：

    2025年4月1日

查看全文
  • D. Zangurashvili

摘要

Abstract

While MacLane’s version of the Kurosh subgroup theorem for free products has been well-known, one of its implications seems to have escaped the attention of the mathematical community. The purpose of this note is to fill this gap by providing this implication. It asserts that a nontrivial normal subgroup of a group is a free factor of this subgroup’s normal closure in the free product of the group with arbitrary nontrivial groups.