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revised Can someone explain Cayley's Theorem step by step?
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Jan
7
awarded  Announcer
Jan
2
comment Suggestions for research in Group Theory
Is there other motivation for study of such Frobenius actions? For one example, check out this paper by yours truly. Long story short, Frobenius groups (and their cousins, 2-Frobenius groups) are important for studying interactions between different Sylow subgroups of a finite solvable group. They also show up a lot when studying finite simple groups, and played a big role in many of the results leading to the Classification.
Dec
16
comment First course in linear algebra and matrices over arbitrary fields
@user26857 Thank you for saying so. I am sure my answers will come more frequently again sometime when I have a period of slow research.
Dec
15
awarded  Famous Question
Dec
12
comment Compressed Sparse Row Format
You may want to consider asking this at StackOverflow instead.
Dec
7
awarded  Notable Question
Nov
6
answered First course in linear algebra and matrices over arbitrary fields
Oct
22
revised Examples of finite nonabelian groups.
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Oct
22
answered What's the Centralizer $ A_{4}/V_{4} $ in $ S_{4} $
Oct
5
awarded  Nice Answer
Oct
2
comment Find all the elements in Dih(2n), n odd, which commute with all other elements
@Rori $r^s\triangleq s^{-1}rs$. It's a group theory shorthand for conjugation.
Sep
28
comment Combinatorial interpretation of identity: $\sum_{j=0}^b\binom{b}{j}^2\binom{n+j}{2b}=\binom{n}{b}^2$
I don't understand your first paragraph. If we take the set $T$ out of $N\cup B$, then isn't that choosing $X$ from an $n$ element set, not an $n+j$ element set?
Sep
11
comment Very generic question about Commutator and Center
Far as textbooks go, the best progression I can recommend is Dummit and Foote followed by Isaacs Finite Group Theory. (I really like Isaacs.) As far as websites go, this one is really the best. Look up some of my old questions and answers, as well as Arturo Magidin, Jack Schmidt, Geoff Robinson. I learned a substantial portion of my group theory from studying their posts.
Sep
11
comment Very generic question about Commutator and Center
$G/H$ is cyclic of prime order because $G/H$ must be abelian (why?) and because the quotient of a group by a maximal subgroup must be simple. In any case, this is overkill, all we really need is for it to be abelian, because there is a result (prove this part yourself, it's easy) that $G/H$ is abelian if and only if $G^\prime\subset H$.
Sep
11
comment Very generic question about Commutator and Center
$H^g$ is group theorist shorthand for $g^{-1}Hg$. $H\unlhd G$ ("$H$ is normal in $G$") because we showed that $H^g=H$.
Sep
11
comment Very generic question about Commutator and Center
Since $K$ is not contained in $H$, $HK$ must be bigger than just $H$. $H$ is a maximal subgroup, though, so the only bigger subgroup of $G$ is $G$ itself. Therefore, $HK$ must be all of $G$. So, any element of $G$ can be written as an element of $HK$, and thus in the form $hk$ for some $h\in H$, $k\in K$.
Sep
10
comment Very generic question about Commutator and Center
@user Sure. If not, let $H$ be a maximal subgroup not containing $G^\prime \cap Z(G)=K$. Then every element of $G$ has the form $g=hk$, so $H^g=H^{hk}=H^k=H\unlhd G$. But then $G/H$ is cyclic of prime order, so $G^\prime\unlhd H$.
Sep
9
awarded  abstract-algebra
Aug
31
awarded  Popular Question