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The Venerable Samuel Handwich, Scholar.


Jul
2
awarded  Curious
Apr
25
awarded  Quorum
Apr
4
revised Orthogonal idempotents from disjoint union in $\text{Spec}(A)$
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Apr
4
revised Non-cyclic finite extensions of fixed fields of infinite order automorphisms of non-algebraically closed fields
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Apr
4
accepted Reference request: Introduction to Finite Group Cohomology
Apr
4
asked Example of $\sum_i a_i\otimes b_i\in M\otimes_AN$ which cannot be written as $a\otimes b$
Mar
30
asked Galois group of $x^5-12x+2$ over $\mathbb{Q}$
Mar
30
asked Did the world experience a “mathematical drought” at any time in history?
Mar
30
accepted Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
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Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
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Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
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Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
added 814 characters in body
Mar
29
comment Explicitly computing the isomorphism class of the tensor product of two finite abelian groups
So, what do I do from here...? (This isn't homework, I'm just stuck, my ring theory sucks.)
Mar
29
asked Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
Mar
29
comment Explicitly computing the isomorphism class of the tensor product of two finite abelian groups
I'm mimicing Servaes' solution to show what you suggested about $\mathbb{Z}_{p^e}\otimes_\mathbb{Z}\mathbb{Z}_{q^f}$. If $p\ne q$, $q^f$ is invertible in $\mathbb{Z}_{p^e}$, so $$a\otimes b=(q^{-f}q^f)a\otimes b=(q^{-f}a)\otimes (q^fb)=(q^{-f}a)\otimes 0=0$$ Check. Now I form $\xi:\mathbb{Z}_p^e\times \mathbb{Z}_p^f\rightarrow \mathbb{Z}_{p^{\min{e,f}}}$, $\phi:(a,b)\mapsto ab$. But I don't understand how to proceed from here. I also don't understand how this map tells me something about the tensor product; it's from the direct. Confused.
Mar
29
accepted Explicitly computing the isomorphism class of the tensor product of two finite abelian groups
Mar
24
asked Explicitly computing the isomorphism class of the tensor product of two finite abelian groups
Mar
1
asked Reference request: Introduction to Finite Group Cohomology
Mar
1
accepted Orthogonal idempotents from disjoint union in $\text{Spec}(A)$