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location Cambridge, UK
age 23
visits member for 1 year, 11 months
seen 9 hours ago

I'm a Part III student in Cambridge.


9h
comment Is this a correct characterisation of natural equivalence?
You might want to check this.
10h
comment Supose that G is a finite abelian group that does not contain a subgroup isomorphic to $Z_p \oplus Z_p$ for any prime $p$. Prove that G is cyclic.
No, $g_1+g_2$, using additive notation for the group operation in $G$. Then $m(g_1+g_2)=mg_1+mg_2=0$.
11h
answered Supose that G is a finite abelian group that does not contain a subgroup isomorphic to $Z_p \oplus Z_p$ for any prime $p$. Prove that G is cyclic.
12h
comment Supose that G is a finite abelian group that does not contain a subgroup isomorphic to $Z_p \oplus Z_p$ for any prime $p$. Prove that G is cyclic.
Let me start with a hint, and let me know if it helps: try induction on the number of terms in the prime factorization of $|G|$.
12h
comment Supose that G is a finite abelian group that does not contain a subgroup isomorphic to $Z_p \oplus Z_p$ for any prime $p$. Prove that G is cyclic.
$|\mathbb{Z}_p\oplus\mathbb{Z}_p|=p^2,$ not $2p$.
2d
comment $L \cap V = \overline{L} \cap V \implies L$ open in $\overline{L}$. [Solved]
Do you mean to say that if the condition holds for all open $V$ that $L$ is open in $\bar L$?
Apr
16
revised What's the relation between prime spectrum and affine space?
edited title
Apr
16
answered What's the relation between prime spectrum and affine space?
Apr
14
comment distance Pure Math graduate programs?
What do you hope to get out of graduate study?
Apr
14
answered Homology/Cohomology of Closed Manfold with $\mathbb{Z}_{2}$ Coefficients
Apr
14
answered Inverse of product of matrices
Apr
14
comment Homology/Cohomology of Closed Manfold with $\mathbb{Z}_{2}$ Coefficients
@Mike, you're right, I don't actually have a way to do that without going through the result we're using here. OP, $H_i(M,\mathbb{Z}_2)$ is a finite-dimensional vector space. $H^i(M,\mathbb{Z}_2)$ is its dual, and finite-dimensional vector spaces over any field are isomorphic to their dual.
Apr
14
answered Behaviour of $\operatorname{Ext}$ with left exact sequences.
Apr
14
comment Homology/Cohomology of Closed Manfold with $\mathbb{Z}_{2}$ Coefficients
Because $\mathbb{Z}_2$ is a field. You can see the implication via universal coefficients or Poincare duality, do you know either one?
Apr
13
comment Consecutive natural numbers
No need to write all the business about supposing. Just say, for instance, "Since 6 is the product of the consecutive natural numbers 1,2,3 and is not divisible by 9, the proposition is false."
Apr
13
answered About the definition of the tensor product of modules
Apr
11
comment If composition with a linear functional is continuous, is the function continuous?
You can extend this to a function weakly continuous everywhere, if you prefer, by making the coordinate functions bump smoothly up to 1 on a small neighbors around $1/n$.
Apr
11
answered If composition with a linear functional is continuous, is the function continuous?
Apr
10
comment If composition with a linear functional is continuous, is the function continuous?
Is $X$ an arbitrary Banach space?
Apr
6
revised Definition of Lie Groups
added 112 characters in body