Double entrys of hikashop plugins after update

I did an update of hikashop and now many plugins appear twice in the installed extensions list, e.g.: "HikaShop user synchronization plugin".
See:
What went wrong?
Could it be, that rights on the filesystem are set too stringently?
What can I do to remove the older entrys?

The user synchronization plugin group had to be changed. So it appears duplicated but that's really two different plugins and the old one has been unpublished automatically during the update. You can just uninstall it via the joomla extension manager (the one of the group "user") if you don't want it.
I don't see any other plugin which appears twice on your plugins list.

thanks for your answer. how can i see, which one is the old plugin? is it the one with the lower id (this would be the one in the folder "user", the other one is in the folder "system")?

It's the one of the group "user", not the one of the group "system". It's indeed the one with the lower id.