I have the second printing of the first edition of Herstein's 'Topics in Algebra', published 1964.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Herstein, Topics in Algebra, page 58

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**