- #1
hitmeoff
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Homework Statement
An operation of a group G on a set S is a function G X S [tex]\rightarrow[/tex] S satisfying:
1. es = s [tex]\forall[/tex]s [tex]\epsilon[/tex] S
2. g(hs) = (gh)s [tex]\forall[/tex]g,h [tex]\epsilon[/tex] G, s[tex]\epsilon[/tex] S
If s [tex]\epsilon[/tex] S, show that the stabilizer of s, defined as the set:
{g [tex]\epsilon[/tex] G | gs = s}
is a subgroup of G
Homework Equations
The Attempt at a Solution
Well from that definition it seems that g must be the identity element of G. Is a set consisting of just the identity not just a group? And since G is a group it includes the identity, thus the set g: {e} is a subgroup of G?