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I am familiar with the term involution for a function that inverts itself, and was wondering if there is a similar term for binary operators like XOR. For example, $a \oplus b \oplus b = a$ for any $a$ and $b$.

Is there a term for operators like these?

Thanks!

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A binary operation $\otimes$ on a set $S$ automatically defines two families of functions from $S$ to $S$: for each $a\in S$ we have $L_a:S\to S:s\mapsto as$ and $R_a:S\to S:s\mapsto sa$. Your condition amounts to saying that these functions are all involutions. –  Brian M. Scott Jan 8 '13 at 21:55
    
en.wikipedia.org/wiki/Involution_(mathematics)#Computer_science I think you just say it that way, "if you fix one parameter, than it's an involution". –  xavierm02 Jan 8 '13 at 22:00

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