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Aug
27
comment Quotient Group question ambiguity about group order
First of all, the binary operation of the group is inherited by the quotient group, but then applied to the "multiplication" of cosets. Your second confusion: you should make a difference between a multiplicative and additive notation of the binary group operation. In multiplicative format $g^k$ Is similar to the additive $g + \dots + g$ ($k$ times).
Aug
27
comment Quotient Group question ambiguity about group order
You are mixing up the concepts of the cardinality (~order) of the coset itself with the order of the coset as a group element in the quotient group.
Aug
25
comment Intersection of subgroup of finite index with infinite subgroup is infinite
$f_1=f_2h$ implies $f_2^{-1}f_1=h \in F \cap H$. Hence$f_1(F \cap H)=f_2(F \cap H)$.
Aug
25
answered Intersection of subgroup of finite index with infinite subgroup is infinite
Aug
25
revised Determine number of elements of order 12 of a group
added 290 characters in body
Aug
24
comment Determine number of elements of order 12 of a group
You should now be able to find out that yourself. One of the coordinates should have order $3$, and another order $4$. So figure out how to construct those elements.
Aug
24
answered Determine number of elements of order 12 of a group
Aug
24
answered p-element centralizing a Sylow p-subgroup
Aug
23
comment Standard notation for indices in group theory?
The books of the group theory authorities (B. Huppert, I.M. Isaacs, D.J.S. Robinson, J. Rose) all use the last one. The straight lines reflect the cardinality of a set, in this case the number of cosets. Similarly, $|G|$ is used for the order (cardinality) of the group $G$. I myself sometimes use another one: index$[G:H]$ too. I certainly would not use the first one with the round brackets. But that is maybe the French school against the Anglo-Saxon conventions.
Aug
22
comment assume $ M/N $ be a chief factor of $ G $. Why $ M/N $ has prime order or order $ 4 $?
Why do you keep asking and changing the same questions?
Aug
21
answered Let $ H/N $ is nilpotent quotient subgroup. Then is $ N $ characteristic in $ H $? If no, then what condition need?
Aug
21
revised Problems with P. Hall theorem proof (The problem involves the use of Frattini's argument)
added 8 characters in body
Aug
21
answered Problems with P. Hall theorem proof (The problem involves the use of Frattini's argument)
Aug
21
comment Find the class equation for the following groups
Can you show how you got these answers, which are by the way correct?
Aug
20
answered If a group $ G$ is not simple does it follow that it is isomorphic to the direct product of two nontrivial groups?
Aug
20
comment A group of order 2p (p prime) and other conditions - prove abelian.
@Ilya.K. You should know that $G/Z(G)$ is cyclic implies $G$ is abelian. Maybe you have not seen this "theorem".
Aug
16
answered Prove $[N(H):H]\equiv [G:H](\mod p)$
Aug
16
comment Given 3 spheres, find the equation of the plane that touches each of the spheres on the same side..?
Excellent hint!
Aug
15
comment Group $G$ acting on $\Omega$ such that each $\alpha \in \Omega$ has unique $p$-element fixing $\alpha$.
Excellent Derek, +1 from me!
Aug
14
answered Prove that Euler phi function is multiplicative by a given theorem