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5

Part of 1993 Hungary-Israel Binational

Problems(1)

H \leq G, |H | = 3

Source: 4-th Hungary-Israel Binational Mathematical Competition 1993

5/27/2007
In the questions below: GG is a finite group; H≤GH \leq G a subgroup of G;∣G:H∣G; |G : H | the index of HH in G;∣X∣G; |X | the number of elements of X⊆G;Z(G)X \subseteq G; Z (G) the center of G;G′G; G' the commutator subgroup of G;NG(H)G; N_{G}(H ) the normalizer of HH in G;CG(H)G; C_{G}(H ) the centralizer of HH in GG; and SnS_{n} the nn-th symmetric group. Let H≤G,∣H∣=3.H \leq G, |H | = 3. What can be said about ∣NG(H):CG(H)∣|N_{G}(H ) : C_{G}(H )|?
group theoryabstract algebrasuperior algebrasuperior algebra unsolved