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Dec
8
awarded  Caucus
Nov
23
comment $|G| + \frac{|G|}{\left|\langle a\rangle\right|} + \frac{|G|}{\left|\langle b\rangle\right|} + \frac{|G|}{\left|\langle ab\rangle\right|}$
Hi @mesel. If a Sylow $p$-subgroup $P$ of a finite group $G$ is cyclic, where $p$ is the least prime divisor of the order of $G$, then it has a normal $p$-complement. This is an application of the transfer homomorphism into $P$. See the sections on the transfer in the books by Robinson or Rotman.
Nov
22
answered $|G| + \frac{|G|}{\left|\langle a\rangle\right|} + \frac{|G|}{\left|\langle b\rangle\right|} + \frac{|G|}{\left|\langle ab\rangle\right|}$
Nov
20
answered Internal and Direct Product question, need help with explanation
Nov
20
comment group of order $36$ abelian
There are $14$ groups of order $36$, but only four of those are abelian. So I think you'd need more information to decide.
Nov
19
awarded  Popular Question
Nov
18
comment Why do proof authors use natural language sentences to write proofs?
In most cases, proofs are meant to be read by people.
Nov
18
comment Nilpotent torsion-free Groups with a fixed Soluble length
No, because $s$ and $n$ are constrained by $n\geq 2^{s-1}$.
Nov
18
comment Order of group from its presentation
Your argument shows that the group is a quotient of the cyclic group of order $5$. You also need to show it is non-trivial.
Nov
7
answered Is there a canonical finite group multiplication table?
Nov
2
comment Placing bricks on Board
Of course, there might very well be some other argument.
Nov
2
comment Placing bricks on Board
The colouring argument you've given here.
Nov
2
comment Placing bricks on Board
That's the standard argument.
Oct
31
comment Group Theory Research Topics [advice]
Take a look at some articles on group theory in the MAA publications (American Mathematical Monthly and Math. Magazine). Some of them propose "projects" at the undergraduate level, and some such articles are themselves the result of undergraduate research. It can also help to find a mentor, if one is available at your school.
Oct
29
comment $2$-groups with odd permutations
Another hint. Try the case in which $H=1$ first; then generalise.
Oct
28
comment Verifying proof that set of all group homomorphisms is an abelian group
Yes, you need to show closure. If you are writing your group $H$ additively, why do you get $f(u)-f(u)=1$ rather than $0$?
Oct
23
answered Surprising identities / equations
Oct
23
answered properties on groups of order $p^2qr$
Oct
23
answered Number of different magmas up to isomorphism
Oct
22
comment Normalizer and centralizer are equivalent when $p$ is the smallest prime dividing $|G|$
@Akaichan, I've edited with the additional information.