Recent content by AgentBased

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    Meaning of colon in group theory, if not subgroup index?

    Evidently, it turns out that it's semi-direct product. The notation comes from the computational algebra system GAP.
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    Meaning of colon in group theory, if not subgroup index?

    I am reading a paper where the author uses colons in the description of groups. Example (not verbatim): "This subgroup is isomorphic to (Z_5 X A_4):Z_2". Several subgroups are described in the same way (as (G_1 x G_2):G_3) throughout the paper. I have seen the colon in G:H to indicate the...
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    Unpacking the Objects in the Category of Sets: Cardinality and Distinctions

    Thank you! I have some background in linear algebra and group theory, but I am just starting categories. I am trying to do some independent study in Categories for the Working Mathematician, and sometimes just a little clarification or explication helps so much when working on the exercises.
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    Unpacking the Objects in the Category of Sets: Cardinality and Distinctions

    Thanks! (You are right, of course, I was being sloppy in using the term "uncountable" as I did.) So suppose you had a function in SET, something like R^2 -> R^2 given by (x_1,x_2) -> (x_1,0). Would this arrow actually go from R^2 to itself, or to some distinct set object indicating the...
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    Unpacking the Objects in the Category of Sets: Cardinality and Distinctions

    Can someone give a quick description of the objects in the category SET? In particular, are sets distinguished by anything more than cardinality (i.e. R^2 has the same cardinality as R--are they distinct objects in SET, or is there just one "uncountable set" object?) Answers/help much...
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