Re: Operations with conjugation in groups

On 25-09-2008 0:00, k.hofmann wrote:

Is it true that conjugation preserves both unions and intersections ?

That is, if A, B are subgroups (or possibly just subsets) of a group G, and g is any element of G, then do either of the following hold?

(1) (A /\ B)^g = A^g /\ B^g

(2) (A \/ B)^g = A^g \/ B^g

where the exponent denotes conjugation by g: X^g = gXg^{-1} (or, if you prefer, X^g = g^{-1} X g) ?

Yes, of course. For *any* bijection _f_ between two sets X and Y, if
A and B are subsets of X, then

f(A \/B) = f(A) \/ f(B) and f(A/\B) = f(A) /\ f(B).

Best regards,

Jose Carlos Santos
.

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