hayyambey's profile - activity

yes i can observe that

N=ker(π)

where π:A×B→B is the Projection map of the second factor B.

The kernel of an homomorphism of groups is always normal, so N is a normal subgroup.

Moreover, by the First isomorphism theorem, it holds

(A×B)/ker(π)≅B ... but is it enough?

yes i can observe that

N=ker(π)

where π:A×B→B is the Projection map of the second factor B.

The kernel of an homomorphism of groups is always normal, so N is a normal subgroup.

Moreover, by the First isomorphism theorem, it holds

(A×B)/ker(π)≅B ... but is it enough?

Let $A$ and $B$ be two groups. Show that set $N$ = { $(a,1): a \in A $ } is the normal subgroup of $A$ x $B$ and
that the $A$ x $B$ $/ N$ quotient group is isomorph to $B$.

if you help me, i'll be exulted.

I want to write the $Bubble Sort$ algorithm on the $GAP$(Groups, Algorithms, Programming), can you help with the algorithm code?

Alhamdulillah, i wrote finding the mersenne primes(by the miller-rabin and lucas- lehmer) last night :) thank you for wanting to help, sir.

i've examined to the Reference book and Tutorial. i want to design two basic program, then compare the times. for example: GCD's two different algorithm.

How can i write special numbers(Mersenne, Fibonacci etc.) or the average or the GCD's two different algorithm in GAP(Group, Algebra and Programming)?

G is a group. $$ x,y \in G , x^4 = 1 ,\ xy = yx^-1, \ x^2=y^2 $$ Can you show the elements of the group in the cayley table? Help me, please.

G is a group. $$ x,y \in G , x^4 = 1 ,\ xy = yx^-1, \ x^2=y^2 $$ Can you show the elements of the group in the cayley table? Help me, please.