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Sep
2
comment What is the most complex mathematical topic?
Not sure what you mean by numbers are easy, given that a whole field of math, number theory, devoted to studying numbers (and I would not say it is easy).
Aug
19
comment The best symbol for non-negative integers
You forgot $\omega$!
Aug
19
reviewed Looks OK Help solving a basic polynomial problem
Aug
18
comment Fundamental Theorem of Abelian Groups
Well, to get you started, are $C_2 \oplus C_2$ and $C_4=C_{2^2}$ the same group? (I am useing "$C$" for cyclic groups). What about the all primes distinct and $G$ being cyclic did you not get?
Aug
18
comment Reference Request: Group Theory via the Group Action Perspective
interest you. Particularly this book which looks interesting, and opens up with semigroups, and has semigroup actions. It looks interesting, but I have not looked at it enough to really comment.
Aug
18
comment Reference Request: Group Theory via the Group Action Perspective
@RexButler I have 4 abstract algebra books on hand and an undergraduate group theory book, and all of them have group actions before Sylow. Pretty sure the majority of algebra books introduce group actions, and use Sylow theorems to show off the power of the idea. It sounds like, from reading your post again, and the comment, that you want something like "abstract algebra for theoretical computer sciences" Is that right? Perhaps this answer has some things that would...
Aug
18
revised Reference Request: Group Theory via the Group Action Perspective
edited tags
Aug
18
comment Reference Request: Group Theory via the Group Action Perspective
What are you looking for exactly, and what direction. I feel like most books with group theory, or on group theory have group actions (the Sylow theorems for example). Plus are you focused on finite groups. Representation of group is all about groups acting on vector spaces. Geometric group theory is basically about groups acting on metric spaces.
Aug
15
comment Gradient of a Frobenium norm cost Function
I am just saying that problem statement questions are normally closed, even just adding a sentence or two about the problem, and/or where it comes from can improve its reception.
Aug
15
reviewed Reviewed Gradient of a Frobenium norm cost Function
Aug
15
comment Gradient of a Frobenium norm cost Function
You should add some context to the question in order to avoid downvotes and the question being closed. Some common way is to show your work on the problem, add what you know about the problem and closely related info. Maybe also add definitions.
Aug
15
answered Is a finite index subgroup of a finitely presented subgroup finitely presented?
Aug
15
comment Cayley graph of a group isomorphic to D6
You know why...
Aug
13
comment Additive group with out element 0 and generator should n't be 1
Oh, I see. How about a bijection $f:\mathbb{Z} \to \mathbb{Z} \setminus \{0\}$ and $f(1) \neq 1$, and do a similar transport of the structure as in the above case... Is that what you are looking for? I am not really sure what you mean by an "additive group", what is that?
Aug
13
comment Additive group with out element 0 and generator should n't be 1
I am not really sure what you mean. Do you want a group on $\mathbb{Z}$, with an operation $\oplus$, which is commutative, but $0$ and $1$ are not identity and generator respectively? If so, choose a bijection $f:\mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}$, where $f(0,0) \neq 0$, then transport the standard group structure onto $\mathbb{Z}$. So $n\oplus m=f(x) \oplus f(y):=f(x+y)$ would define an abelian group on $\mathbb{Z}$. If that is not what you are looking for, then you need to make your question more clear.
Aug
12
comment Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
It may use Lebesgue integration... huh.
Aug
12
comment Thermodynamics about turbines
Hopefully the people that follow fluid dynamics won't murder me for sending this question there (I don't know anything about fluid dynamics...). Although hopefully this question wont be around long enough for them to find out, they didn't even remove the question numbering. (I got to this question thinking it would be some cool question connecting thermodynamics and group theory :(, I was mistaken)
Aug
12
revised Thermodynamics about turbines
edited tags
Aug
11
revised Showing that a one-relator group, $\langle a,b \mid W \rangle$, is not a free product.
Added a bit on how to find words that split the group into free factors
Aug
11
comment General Isomorphism, for all algebraic structures
@JoshChen There are examples of continuous bijections between spaces with the same topology that are not homeomorphisms. For example here and here.