2020-01-02 17:56:39 +0200 commented question The question in the name of Normal Subgroup and Isomorphism 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? 2020-01-02 17:55:42 +0200 answered a question The question in the name of Normal Subgroup and Isomorphism 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? 2020-01-01 16:04:29 +0200 asked a question The question in the name of Normal Subgroup and Isomorphism 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. 2019-12-30 16:07:56 +0200 asked a question Writing the Bubble Sort on the GAP I want to write the $Bubble Sort$ algorithm on the $GAP$(Groups, Algorithms, Programming), can you help with the algorithm code? 2019-11-14 20:20:31 +0200 commented question Functions in GAP Alhamdulillah, i wrote finding the mersenne primes(by the miller-rabin and lucas- lehmer) last night :) thank you for wanting to help, sir. 2019-11-13 16:21:04 +0200 commented question Functions in GAP 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. 2019-11-12 21:30:04 +0200 asked a question Functions in GAP 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)? 2019-11-11 18:30:27 +0200 asked a question The Cayley Table Question 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. 2019-11-11 18:30:27 +0200 asked a question The Cayley Table Question 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.