Two questions

Googling around, I have come on several claims that there are no
non-trivial injectives in the category of groups (e.g., Mac Lane in the
1950 Duality for groups paper credits Baer with an elegant proof, but
gives no hint of what it might be and Baer's earlier paper on injectives
doesn't mention it).  I have not come on any proof of this, however.

Somewhere I have seen a proof that all monics in the category of groups
are regular.  I think it was in a paper by Eilenberg and ??? and it needed
a special argument if there were elements of order 2.  Can someone help me
find this?

Michael

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