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7.7 Let G be a group and let a € G. Define a function f: G→G by f(x)=axa- for all xEG. Is f one-to-one? Is f onto? = axa

7.7 Let G be a group and let a € G. Define a function f: G→G by f(x)=axa- for all xEG. Is f one-to-one? Is f onto? = axa

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Only 7.7 please.
**7.7** Let \( G \) be a group and let \( a \in G \). Define a function \( f: G \rightarrow G \) by \( f(x) = axa^{-1} \) for all \( x \in G \). Is \( f \) one-to-one? Is \( f \) onto? **7.8** Let \( G \) be a group, and let \( f(x) = x^{-1} \) for all \( x \in G \). Is \( f \) a function from \( G \) to \( G \)? If so, is it one-to-one? Is it onto?
Transcribed Image Text:**7.7** Let \( G \) be a group and let \( a \in G \). Define a function \( f: G \rightarrow G \) by \( f(x) = axa^{-1} \) for all \( x \in G \). Is \( f \) one-to-one? Is \( f \) onto? **7.8** Let \( G \) be a group, and let \( f(x) = x^{-1} \) for all \( x \in G \). Is \( f \) a function from \( G \) to \( G \)? If so, is it one-to-one? Is it onto?
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