Recent content by barbutzo

well, first, since H is normal, gBg^-1 is a subgroup of H. second, it's also a p-Sylow subgroup of H, so it's conjugate to B. Oh! so it's also of the form hBh^-1! great, I'll take it from here. thanks!

Homework Statement Let G be a finite group, and H be a normal subgroup of G. Let B be a p-Sylow subgroup of H, for some p dividing |H|. Show that G=HN_G(B). (N_G(B) is the normalizer of B in G, that is the biggest subgroup of G which contains B and B is normal in it. Equivalently...

OK, I think I've worked out my problem. Is it considered acceptable here to post my final solution to my question?

The meaning of identity here can be seen this way - suppose we start with one handlebody, and duplicate it to create the second one. Now the identity means mapping each point in the original to the point it was duplicated to in the second.

Hello all, I have a question I'm having a hard time with in an introductory Algebraic Topology course: Take two handlebodies of equal genus g in S^3 and identify their boundaries by the identity mapping. What is the fundamental group of the resulting space M? Now, I know you can glue two...