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Aug 2, 2023 at 19:48 vote accept Sam Forster
Aug 2, 2023 at 19:48 comment added Sam Forster @TimothyChow Thanks, I didn't know if that would be considered spam.
Aug 2, 2023 at 12:05 comment added Timothy Chow @SamForster You can still accept this answer and re-post your second question separately.
Aug 1, 2023 at 15:34 comment added Sam Forster Thank you very much! In hindsight I should have split my questions into two posts, as my post is technically still open despite your answer. But this settles my first question, thank you.
Aug 1, 2023 at 13:58 comment added Joachim König I think the notion of "completion" in the question is intended to include iteration, so that the embedding would be into an iterated wreath product, not a direct product, but the argument still works in the same way.
Aug 1, 2023 at 13:39 history answered Peter Mueller CC BY-SA 4.0