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Tag Archives: group actions
Intermediate Group Theory (3)
Automorphisms and Conjugations of G We’ve seen how groups can act on sets via bijections. If the underlying set were endowed with a group structure, we can restrict our attention to bijections which preserve the group operation. Definition. An automorphism of … Continue reading
Posted in Notes
Tagged advanced, automorphisms, conjugate, group actions, group theory, semidirect products
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Intermediate Group Theory (2)
This is a continuation from the previous post. Let G act on set X, but now we assume that both G and X are finite. Since X is a disjoint union of transitive Gsets, and each transitive Gset is isomorphic to G/H for some subgroup H ≤ G, it follows that … Continue reading
Posted in Notes
Tagged advanced, cauchy's theorem, group actions, group theory, normaliser, sylow theorems
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