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Proposition: Criteria for Subgroups

Let \((G,\ast)\) be a group and \(H\) be a non-empty subset \(H\subseteq G\).

1. \(H\) is of a subgroup of \(G\), if and only if \(a\ast b^{-1}\in H\) for all \(a,b\in H\).
2. \(H\) is of a subgroup of \(G\), if and only if \(a\ast b^{-1}\in H\) for all \(a,b\in H\).

Table of Contents

Proofs: 1

Mentioned in:

Explanations: 1
Proofs: 2 3 4 5
Solutions: 6

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References

Bibliography

1. Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013
2. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013