Paul Plummer
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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.