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## Main Question or Discussion Point

I have the second printing of the first edition of Herstein's 'Topics in Algebra', published 1964.

On page 58 near the middle of the page there is a paragraph that begins:

Let G be a cyclic group ...

The author writes

[tex]\phi:a^i \rightarrow a^{2i}[/tex]

and later

[tex]x^{-1}a^ix = \phi(a)^i = a^{3i}[/tex]

The next paragraph makes it clear that he means:

[tex]x^{-1}a^ix = \phi^i(a) = a^{3i}[/tex]

But it doesn't seem true to me. for instance if i = 1, then no matter how I write it, I get:

[tex]\phi(a) = a^3[/tex]

but by the definition of phi,

[tex]\phi(a) = a^2[/tex]

What gives?

On page 58 near the middle of the page there is a paragraph that begins:

Let G be a cyclic group ...

The author writes

[tex]\phi:a^i \rightarrow a^{2i}[/tex]

and later

[tex]x^{-1}a^ix = \phi(a)^i = a^{3i}[/tex]

The next paragraph makes it clear that he means:

[tex]x^{-1}a^ix = \phi^i(a) = a^{3i}[/tex]

But it doesn't seem true to me. for instance if i = 1, then no matter how I write it, I get:

[tex]\phi(a) = a^3[/tex]

but by the definition of phi,

[tex]\phi(a) = a^2[/tex]

What gives?