Kernel of a homomorphism
- Thread starter Kurchi
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D
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Why NOT?
Please show us what you have tried and exactly where you are stuck.
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pka
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\(\begin{align*}\varphi ({g^{ - 1}}hg) &= \varphi ({g^{ - 1}})\varphi (h)\varphi (g) \hfill \\
& = \,\varphi ({g^{ - 1}})\bar e\varphi (g) \hfill \\
& = \,\varphi ({g^{ - 1}})\varphi (g) \hfill \\
& = \varphi ({g^{ - 1}}g) \hfill \\
& = \varphi (e) \hfill \\
& = \bar e \hfill \\
\end{align*} \)
& = \,\varphi ({g^{ - 1}})\bar e\varphi (g) \hfill \\
& = \,\varphi ({g^{ - 1}})\varphi (g) \hfill \\
& = \varphi ({g^{ - 1}}g) \hfill \\
& = \varphi (e) \hfill \\
& = \bar e \hfill \\
\end{align*} \)