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.
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.