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Which is the stabilizer of a vertex in group theory?
The stabilizer of a vertex is the cyclic subgroup of order 2 generated by re ection through the diagonal of the square that goes through the given vertex. (c) Gis the dihedral group D. 10 or order 10. The orbit of any vertex is the set of all 5 vertices of the pentagon.
Which is the centre of a group G?
The centre of a group G, denoted Z(G) (from the german word ‘zen- trum’), is the set of all those elements in the group which commute with every element of the group. Thus Z(G) := fz2Gjzg= gzfor all g2Gg: Prove that Z(G) is a subgroup of G, for any group G. Solution: Clearly 1 2Z(G), so Z(G) is nonempty.
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