On the Cohopficity of the Direct Product of Cohopfian Groups

Abstract

Suppose both A and B are cohopfian groups. Then A × B is cohopfian if A is either extremely noncommutative and torsion free, or finite Abelian, or finite simple.

Key Words:

• Cohopfian groups
• Extremely noncommutativity
• Finite Abelian groups
• Finite simple groups

AMS Subject Classification:

• 20F65
• 20K30

ACKNOWLEDGMENTS

I would like to thank Professor Shicheng Wang for suggesting this question, informing the definition of extremely noncommutativity, and some helpful conversations. I also would like to thank Lujun Jia for his many valuable comments and pointing out an error in an earlier version of this article.

Notes

Communicated by A. Yu. Olshanskii.