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Feb 15, 2017 at 13:13 comment added user103474 Ok, thanks a lot! It was easy and this example is also in the book I mentioned. Maybe it is true that always the number of simple modules of $A\#kH$ is at most the number of simple modules of $A$.
Feb 15, 2017 at 13:10 vote accept user103474
Feb 15, 2017 at 12:10 history answered Jeremy Rickard CC BY-SA 3.0