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7m
answered Normal group and commutator subgroup question
10h
comment Find the coordinates of the point(s) at which the tangent to the curve is parallel to the x-axis.
Hint: can you find the coordinates of the top of the parabola, even without knowing derivatives?
10h
reviewed Approve Find the coordinates of the point(s) at which the tangent to the curve is parallel to the x-axis.
1d
comment If $Ha\subseteq Kb$ for some $a,b\in G$, show that $H \subseteq K$ (Proof Verification)
You are welcome!
1d
comment Prove that the maximal normal Abelian subgroup $A$ of metabelian group is equal to $C_G$($A$).
@Whacka: good hints!
1d
answered If $Ha\subseteq Kb$ for some $a,b\in G$, show that $H \subseteq K$ (Proof Verification)
1d
answered Number of Sylow $p$-subgroups of a direct product of groups
2d
comment Example of non-commuting conjugacy classes?
@DJF - yes absolutely, good observation! The notion of commutativity concerns sets/conjugacy classes, rather than elements.
2d
comment If G is a group not cyclic then its order can be:
This is kind of folklore, see for example here ysharifi.wordpress.com/2010/12/13/… or arxiv.org/pdf/1104.3831v1.pdf
2d
answered If G is a group not cyclic then its order can be:
2d
comment About the equation $|HK|=\frac{|H|.|K|}{|H\cap K|}$
OK, fair enough - btw you should infer that "for all subgroups $B$ having a non-empty intersection with $A$"
2d
comment About the equation $|HK|=\frac{|H|.|K|}{|H\cap K|}$
@Tobias Nice question - this warrants a separate post!
2d
comment About the equation $|HK|=\frac{|H|.|K|}{|H\cap K|}$
Ah oversaw that ... thanks. Will correct.
2d
revised About the equation $|HK|=\frac{|H|.|K|}{|H\cap K|}$
added 143 characters in body
2d
answered Give an example of a group G with a subgroup H and a prime p such that a Sylow p-subgroup of H is not a Sylow p-subgroup of G
2d
answered About the equation $|HK|=\frac{|H|.|K|}{|H\cap K|}$
May
2
answered Example of non-commuting conjugacy classes?
May
2
comment Prove/disprove: Let $g\in G$ satisfy $o(g) = n$ and $g^m\in H$, where$ (n,m)=1.$ Then $g \in H.$
Bill, $H$ does not have to be normal, so $G/H$ could be meaningless ...
May
2
comment Find an example of a group morphism
This is something you yourself should find out! Hint - find an element of $S_4$, say $\tau$, such that $\tau^{-1}(123)\tau \notin A_3$. That is not too difficult.
May
2
comment Find an example of a group morphism
Ah, OK. Well, you can view $S_3$ as a subset of $S_4$. So your $f$ would be $f(\sigma)=\sigma$. This embedding is obviously a (trivial) homomorphism. That is, the elements of $S_3$ are then part of a bigger group in which $H_1$ loses its normality.