(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 A^{g}is a subgroup of G.

3. 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 A^{g}(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 A^{g}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?

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# Homework Help: Subgroup math properties help

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