Tuesday, August 18, 2015

A Wrinkle in Terms

Filed under: General,Geometry — m759 @ 8:23 AM

The phrase “the permutation group Sn” refers to a
particular  group of permutations that act on an
-element set N— namely, all  of them. For a given n ,
there are, in general, many  permutation groups that
act on N.  All but one are smaller than S.

In other words, the phrase “the permutation group Sn
does not  imply that “Sn ” is a symbol for a structure
associated with n  called “the  permutation group.”
It is instead a symbol for “the symmetric  group,” the largest
of (in general) many permutation groups that act on N.

This point seems to have escaped John Baez.

For two misuses by Baez of the phrase “permutation group” at the
n-Category Café, see “A Wrinkle in the Mathematical Universe”
and “Re: A Wrinkle…” —

“There is  such a thing as a permutation group.”
— Adapted from A Wrinkle in Time , by Madeleine L’Engle

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