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Jan 31 at 22:22 comment added R W One can use power series in the group algebra for other functions (logarithm or even directly square root) - see the book I quoted.
Jan 23 at 15:13 comment added dohmatob Thanks (upvoted). This looks like a very elegant and general approach. As a sanity check, what does it concretely imply for my question, even in the case $p=2$ or $p=3$ ? Thanks in advance.
Jan 23 at 14:18 history answered R W CC BY-SA 4.0