A group is an algebraic structure consisting of a set of elements together with an operation that satisfies four conditions: closure, associativity, identity and invertibility. Group theory studies groups.

learn more… | top users | synonyms (2)

12
votes
2answers
2k views
+100

Normal subgroups of free groups: finitely generated $\implies$ finite index.

I am looking at what should be a simple exercise in geometric group theory. I have reduced the problem to just completing an exercise from Hatcher, Section 1.B page 87: 7. If $F$ is a finitely ...
1
vote
0answers
27 views
+50

Hypercenter is the intersection of normalizers of Sylow subgroups.

I'm trying to prove that the intersection of the normalizers of the Sylow subgroups of a [finite] group $G$ is equal to its hypercenter, i.e., $$Z_\infty(G)=\bigcap\limits_{S\in ...