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Results tagged with gr.group-theory
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user 99545
Questions about the branch of algebra that deals with groups.
6
votes
1
answer
402
views
Infinite simple group of exponent a power of 2
Let G be a simple group of exponent 2^n for n>1. Is G necessarily finite? If not, what is an example of an infinite simple group of exponent a power of 2?
- 457
4
votes
3
answers
596
views
Regular orbits for automorphisms of finite simple groups
Let $G$ be a finite group and $f$ be an automorphism of $G$. We say that $f$ has a regular orbit if there exists $x\in G$ such that $|x^f|=|f|$. If $G$ is abelian it is known that every automorphism o …
- 457
10
votes
4
answers
1k
views
Conjugation by elements of subgroups
Let $G$ be a group generated by a conjugacy class $C$. I am interested in studying this property:
for every $x,y\in C$ there exists $h\in \langle x,y\rangle$ such that $y=hxh^{-1}$.
Basically the prop …
- 457