Recent content by margaret23

Show that Z3 X Z5 is isomorphic to Z15 (where Zn is like the intergers mod n) i m not sure if i m proving it right.. if i first right out Z3 x Z5 ={(1x1), (1X2),(1x3),(1x4), (1X5), (2X1),(2x2),(2x3), (2x4), (2X5), (3x1), (3x3),(3x3),(3x4), (3X5)} Z15={1,2,3...15} both of which have 15...

I know I am making a stupid mistake but I am not sure what it is... Find an equation for the plane tangent to the torus X(s,t)=((5+2cost)coss, (5+2cost)sins, 2sint) at the point ((5-(3)^1/2)/(2)^1/2, (5-(3)^1/2/(2)^1/2, 1). First I have to find what s and t are in order to sub them in for...

thanks :).. i got it now

umm ok .. so i get that aabb must also =e .. but I am not sure how to get abab

Could you also help me start this question show that if a^2 = e for all a in G then G must be commutative. (where e is the identity) thanks

Thanks soo much

ps.. thanks

my counter example to the second one is the diherdral group containing the permentation of 3 elements. i m having trouble rapping my mind around how this is cyclic.. i ve delt a lot with simpler groups like the intergers mod n , i don't quite understand what makes my counter example cyclic if...

Thanks for the help on the second one .. it makes sense now.. for the first question about proving that if all subgroups are cyclic then the group is cyclic. I would think that its true however i do not know how to start the proof. Could you put me on the right track again?? thanks

the question doesn't state that its not including the whole group as a subgroup, however i think that its safe to assume that they want it proved without. I' m thinking from what i know about groups that the first one is true.. and that the second one is false. I think that the second...

I m having trouble with a couple group theory proofs. I just have no clue how to start. If u could put me on the right path that would be great. first prove of disprove that if every subgroup of a group G is cyclic, then G is cyclic. and second prove or disprove that every group X of...