I admit having known him.

My grammar book says it is wrong, but it doesn't explain why. However, it says "I admit knowing him." is correct. May I ask why is "I admit having known him." wrong? I'd appreciate your reply. Thank you!
Logically, it is questionable, since once knowing someone, it is hard or impossible to 'un-know' them.
I think you have a good grammar book and MM makes a very good point.
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Perhaps he died.

We usually don't say that we know someone who is dead.

Best wishes, Clive
Thanks, I understand now.
"I admit to having known him for a while" would be fine.

"Admit to" is better English. Also, the above sentence uses the Present Perfect ("have known" instead of "know", which is the Present Simple). With sentences in the Present Perfect, however, a time period which persists until the present moment must be stated.
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... must be stated or implied / understood.