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Tag Archives: conjugate
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 (1)
Given a group G, we wish to find out more about its properties. Questions include: what subgroups does it have? And normal subgroups? How many elements of order m does it have (where m must divide the order of G if the latter is finite)? … Continue reading
Posted in Notes
Tagged advanced, conjugate, Gsets, group action, isotropy group, stabiliser group, transitive action
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Casual Introduction to Group Theory (1)
Introduction Last year, I created a blog which was supposed to introduce concepts to abstract algebra in a systematic manner. Though I was reasonably happy with the end result, I got the sneaky feeling upon completion that the end product … Continue reading
Posted in Notes
Tagged 15 puzzle, abstract algebra, basic, casual, conjugate, group theory, order, permutations, rubik's cube, symmetries
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