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In the previous chapter, we calculated concrete examples of homomorphisms. Given a group homomorphism \(\varphi :G\to H\) , the factor group \(G/\ker \varphi \) and \( \operatorname {\mathrm {Im}}\varphi \) seem in some sense identical. We will give this intuition a rigorous formulation in this chapter.

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Isomorphism Theorems for Groups

  • 章节

  • 发表日期：

    2026年

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  • Shuichi Yukita

摘要

In the previous chapter, we calculated concrete examples of homomorphisms. Given a group homomorphism \(\varphi :G\to H\) , the factor group \(G/\ker \varphi \) and \( \operatorname {\mathrm {Im}}\varphi \) seem in some sense identical. We will give this intuition a rigorous formulation in this chapter.