This article is cited in 1 paper

On groups with isomorphic holomorphs

I. Kh. Bekker, V. N. Nedov

Tomsk State University

Abstract: Groups with isomorphic holomorphs are said to be holomorphically isomorphic. The following problems are treated.

• 1) What Abelian groups have the property that their holomorphic isomorphism implies the isomorphism of the groups themselves?
• 2) Does holomorphic isomorphism of two groups, one of which is Abelian, imply the commutativity of the other group?

Classes of groups are selected for which the answers to these questions are positive.

UDC: 512.541

Received: 02.10.1995

DOI: 10.4213/mzm1616

 English version: Mathematical Notes, 1997, 62:3, 288–295

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