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Jul
27
revised Gysin sequence for the sphere bundle $B[O_a \times O_B]^+ \to BO_a \times BO_b$?
added 1 character in body; edited title
Jul
24
comment Ring Theorem Proof Example
Write $0=0+0$, and use the distributive property.
Jul
24
comment Homeomorphism and Mapping
@AlecTeal I know, the groups $S$ and $J$ were introduced, but the codomain of $f$ was $M$. It's been fixed now.
Jul
22
answered Prove or disprove $\max\{a,\max\{b,c\}\}=\max\{\max\{a,b\},c\}$
Jul
22
answered if $H \leq G$ has index 2, then $a^2\in H$ for every $a\in G$
Jul
20
comment What exactly are maps from $(I, \partial I) \to (I, \partial I) $?
Perhaps it's a map of pairs? A function $f\colon (X,A)\to (Y,B)$ is said to be a map of pairs if $f\colon X\to Y$ is such that $f(A)\subseteq B$, where $A\subseteq X$ and $B\subseteq Y$.
Jul
18
comment Every normal subgroup is the kernel of some homomorphism
No, you more or less have it, the kernel of $\pi\colon G\to G/N$ is $N$. No need to worry about $\pi^{-1}$, or if it exists.
Jul
14
comment group $G$ of order $312$. show that G is not simple
@Prism Done! ${}$
Jul
13
comment Cosets of Subgroup Example
@KevinMeredith Those are just sets, and sets are equal if their elements are the same, there is no inherent order for the elements in a set.
Jul
13
comment Cosets of Subgroup Example
I guess what may be confusing is that the notation $aH$ is basically the set you get when you compose $a$ with each element of $H$ by the group operation, whatever it may be. For $\mathbb{Z}_4$, this operation is usually denoted $+$, so the the coset notation is a little different.
Jul
13
comment Cosets of Subgroup Example
Think of $H+a$ as the set you get when you add $a$ to each element in $H$. So for example $H+2=\{0+2,2+2\}=\{2,0\}=\{0,2\}$.
Jul
12
comment group $G$ of order $312$. show that G is not simple
You might want to post a brief answer that the Sylow $13$-group is normal, so this question moves off the unanswered list.
Jul
5
revised Quantity of elements of order $d$ in $Z_n$, with $d \mid n $
added 8 characters in body
Jul
2
answered Cartan integers are preserved by isomorphism?
Jun
27
answered If $I$ and $J$ are distinct ideals in ring $R$ and $f:R \to R'$ is a homomorphism then is $f(I) = f(J)$?
Jun
27
comment If $I$ and $J$ are distinct ideals in ring $R$ and $f:R \to R'$ is a homomorphism then is $f(I) = f(J)$?
Are you trying to disprove the claim in the title, or prove the claim in the body of the question that the books states?
Jun
26
answered Every base of a root system arises as indecomposable positive roots of a regular element?
Jun
25
comment Homotopy equivalence of $S^{2} \vee S^1$ to $S^{2} \cup A$ where A is a line segment joining noth and south poles
This is shown in Chapter 1, Section 2, Example 2 of "Two Criteria for Homotopy Equivalence" in Hatcher. (Not sure about numbering since I'm looking at a hardcopy from 1999.) It uses the fact that if $(X,A)$ satisfies the homotopy extension property with $A$ contractible, then $X$ and $X/A$ are homotopy equivalent by the quotient map. This is proven in Prop 0.2. (Again, not sure of current numbering.)
Jun
22
answered Equality on pg. 40 of Humphreys's Lie Algebras, $\kappa(t_\lambda,t_\mu)=\sum_{\alpha\in\Phi}\alpha(t_\lambda)\alpha(t_\mu)$?
Jun
13
revised How to tell if 3 connected points are connected clockwise or counter-clockwise?
edited tags