Test

mermaid

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sequenceDiagram
  Alice->>John: Hello John, how are you?
  loop Healthcheck
      John->>John: Fight against hypochondria
  end
  Note right of John: Rational thoughts!
  John-->>Alice: Great!
  John->>Bob: How about you?
  Bob-->>John: Jolly good!

LaTeX

The homomorphism \(f\) is injective if and only if its kernel is only the singleton set \(e_G\), because otherwise \(\exists a,b\in G\) with \(a\neq b\) such that \(f(a)=f(b)\).