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I am looking for a text that helps to learn abstract algebra visually rather than theoretically. I have encountered a book of linear algebra namely Geometric Linear Algebra by I-Hsiung Lin. It does a great job in explaining the concepts with the help of diagrams and enables the reader to visualize the topic better. But I do not know about any similar book for abstract algebra especially for the topic group theory about how to visualize the structure of a group, subgroups embedded within a group, cosets, visualizing isomorphisms, homomorphisms, the structures of kernel and image groups of a homomorphism. I had started reading Nathan Carter's visual group theory but I think the way it develops the topic is not suiting me. Can someone suggest me a good book to satisfy my demand (sans N.Carter's book).

user26857
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Kishalay Sarkar
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  • Take a look at https://math.stackexchange.com/q/1233705 – Jean Marie Dec 26 '19 at 10:04
  • There's a book called Visual Group Theory, but I haven't read it so I don't know anything about it. – littleO Dec 26 '19 at 10:11
  • I think the issue is that groups are inherently algebraic structures. They don't have any geometric meaning intrinsically embedded in them. Unless, you embue such a meaning forcibly. – Someone Dec 26 '19 at 10:41
  • Most of the diagrams you could make would be very close to the set theoretic nature. Unless, you can talk about groups that can be provided with a topological structure. – Someone Dec 26 '19 at 10:44
  • @JeanMarie Do you have any book in suggestion? – Kishalay Sarkar Dec 26 '19 at 12:46
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    @Mann On the other hand, Klein's Erlangen Program suggests that groups are highly geometrical, so much so that you could characterize geometries with groups. But if the poster's meaning is "2D or 3D geometry in the reals that I can picture in my head" then yeah, many groups will be senseless. – rschwieb Dec 26 '19 at 14:54
  • I guess, it boils down to a way of thinking. I am not saying that Groups can't be given a geometrical meaning. But, in a sense, I am saying that they are first and foremost algebraic structures. Of course, A lot of algebra can be used to describe geometry. So, I was curious about what the "structure" of an arbitrary group as given by group axioms could entail toward geometry. As said in the question, I don't think the kind of visualization the user is asking can be directly inferred. Without providing geometric meaning from other domains. – Someone Dec 26 '19 at 14:59
  • Are you aware of the classical book "Icosahedron" by the famous 19th century mathematician Klein ? https://mathoverflow.net/q/9474 gives connections. – Jean Marie Dec 26 '19 at 15:42

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