- #1
roam
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Homework Statement
Let G be a group and let [tex]A \leq G[/tex] be a subgroup. If [tex]g \in G[/tex], then [tex]A^g \subseteq G[/tex] is defined as
[tex]A^g = \{ a^g | a \in A \}[/tex] where [tex]a^g = g^{-1}ag \in G[/tex]
Show that Ag is a subgroup of G.
The Attempt at a Solution
I will use the one step subgroup test. First I have to identify the property that distinguishes the elements of Ag (a defining condition). I don't see what's the binary operation so I can't tell what this property is...
If I knew this property, I would prove that the identity has this property, so that Ag is nonempty. Then I'd use the assumption that a and b have that property to show that ab-1 has this property. Could anyone help me out to see what the property of this group is?
P.S. I think the identity for this group is "1", right?