- #1
Jimmy Snyder
- 1,127
- 21
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?