乘积- 1序列的模群的同构问题

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-03-06 DOI:10.1112/blms.70042

Alfred Geroldinger, Jun Seok Oh

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引用次数: 0

摘要

设g1 $G_1$和g2 $G_2$是扭转群。证明了g1 $G_1$和g2 $G_2$上的积一序列的模群是同构的当且仅当群g1 $G_1$和g2 $G_2$是同构的。这在阿贝尔群中是已知的。

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On the isomorphism problem for monoids of product-one sequences

Let $G_{1}$ and $G_{2}$ be torsion groups. We prove that the monoids of product-one sequences over $G_{1}$ and over $G_{2}$ are isomorphic if and only if the groups $G_{1}$ and $G_{2}$ are isomorphic. This was known before for abelian groups.