Recent content by Monkeyfry180

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    High School How Can You Verify the Definitions of Homomorphism and Subgroup?

    Gracias
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    How Do Community Members Feel About Our Research?

    Sounds great thank you
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    The Power of Group Theory to Success

    Huzzah.
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    Graduate Understanding the Direct Product of Groups: Applying Group Theory Axioms

    Alright, I just did the proofs and got the same answer, thank you so much. Also, using those same values, if f1: G1 --> G is defined by f1(g) = (g, e2), how can we prove that f1 is an homomorphism, one to one, and onto?
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    Graduate Understanding the Direct Product of Groups: Applying Group Theory Axioms

    It's easy to talk myself through associativity, but the other three are giving me trouble
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    Graduate Understanding the Direct Product of Groups: Applying Group Theory Axioms

    Well let's say we have the two groups G1 and G2 with operations *1 and *2, respectively, and we do the cartesian product to get G1 x G2 = { (a,b) : a is an element of G1, and b is an element of G2} = G with the binary operation, * let's say, defined by (a,b) * (c,d) = (a *1 c, b *2 d)...
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    Graduate Understanding the Direct Product of Groups: Applying Group Theory Axioms

    How do we know that the cartesian product of any two groups is also a group using the axioms of group theory?