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Jul
30
comment Squaring is linear in Galois Field $2$
It is not true that squaring is linear in all fields on characteristic two -- only that it is additive.
Jul
30
comment Making sense of the term $H^1(N,A)^{G/N}$ in the inflation-restriction exact sequence.
See Benson - Representations and Cohomology II section 3.5 for a description of how this action is defined. Briefly, you take a $kG$-projective resolution of $k$ which is a $kN$-projective resolution by restriction, so can be used to calculate $H^1(N,A|_N)$. Then the space of $N$-homs from this resolution to $A$ is a $G$-module ($(g\cdot f)(q)=gf(g^{-1}q)$), but $N$ acts trivially, hence it becomes a $G/N$-module. This induces an action on the Ext-groups.
Jul
29
comment A problem about isomorphism in module theory
Standard counterexample for questions like this: $R=\mathbb{Z}$, $B= \mathbb{Z} \oplus \mathbb{Z} \oplus \cdots$, $\ker g = \mathbb{Z} \oplus \mathbb{Z} \oplus 0 \oplus 0 \oplus \cdots$, $\operatorname{im} f = \mathbb{Z} \oplus 0 \oplus 0 \oplus \cdots$
Jul
29
comment In general, how do you construct a nontrivial representation of a group?
Every group has a regular representation, which is nontrivial so long as the group is nontrivial.
Jul
28
comment Hint to find the order of the group of $2\times 2$ matrices under multiplication
math.stackexchange.com/questions/1200622/… math.stackexchange.com/questions/901654/… math.stackexchange.com/questions/296047/… ...
Jul
28
revised Is “Categories and Sheaves” a good followup to Aluffi's “Algebra: Chapter 0”?
added 20 characters in body
Jul
23
comment MAGMA and groups of order 0
If your object is called g, call Type(g); It will say something like GrpPerm. Go to the handbook section for the function Order : GrpPerm -> RingIntElt (or index) and see if it specifies what 0 means. If not only people with inside Magma knowledge can help you (it's closed source).
Jul
22
comment MAGMA and groups of order 0
Certainly for some types of group 0 is to be interpreted as infinity: see magma.maths.usyd.edu.au/magma/handbook/text/779#8622 On the other hand, sometimes it returns 0 if it can't either find the order or prove it is infinite magma.maths.usyd.edu.au/magma/handbook/text/797#8917 You need to check the handbook for the particular type of group on which you are calling Order or #
Jul
21
awarded  Nice Answer
Jul
14
answered Is it possible to put an equilateral triangle onto a square grid so that all the vertices are in corners?
Jul
11
comment What are “instantaneous” rates of change, really?
@Henning NSA doesn't require you to shift back and forth between reals and hyperreals, for example there are no hyperreals in the IST approach.
Jul
10
reviewed Approve Evaluating an indefinite integral with a square root in the denominator
Jul
8
comment Recommendation for books on topology (light reads)
A topological picturebook by George Francis?
Jul
8
comment arithmetic with quantum integers
The relationship is that the first $[n]_q$ is equal to $q^{-n+2}\{ n\}_{q^2}$ where the curly brackets denote the second kind of $q$-integer. This means you can derive multiplication formulas for the first kind from ones for the second.
Jul
8
comment Prove or disprove $A_5$ has a subgroup that isomorphic to $\mathbb{Z}_6$
math.stackexchange.com/questions/1246662/…
Jul
8
comment Noncyclic Abelian Group of order 51
There is no need for the Sylow theorems here! The result you mention is Cauchy's theorem, much simpler than Sylow's theorems.
Jul
4
comment Acting algebraically
Is G an algebraic group? Is V a variety?
Jul
1
comment Relations between $R^fG$ and either $\mathbb{C}^fG$ or $\mathbb{Z}^fG$.
What do $\bar f$ and $\tilde f$ really mean? The obvious interpretation of $f$ is as (the class of) a map $G \times G \to R^\times$ -- how does this give a map $G \times G \to \{\pm 1\}$?
Jun
25
comment Is there a short symbol that denotes integration?
People write $f^{(r)}$ for $f$ differentiated $r>0$ times (no indication of which variable you differentiate with respect to). You could just extend this to negative $r$, though it is definitely not standard notation.
Jun
24
comment How to determine non trivial homomorphisms
There is no algorithm that will solve all of these problems, so the method you should use depends entirely on the groups or rings involved.