Talk:Frattini subgroup

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Talk:Frattini subgroup

[edit] example : p²

Why is the example given as p²? Why not just p? Or n? Any cyclic group has Φ(G)=G, so why the fancy-ness? I know it's petty, but it could also confuse people... 88.109.188.112 08:47, 10 May 2007 (UTC)

No finite or cyclic group has Phi(G)=G. The smallest group with nontrivial Frattini subgroup is the cyclic group of order four. It has a unique maximal subgroup, a cyclic subgroup of order two, which is therefore its Frattini subgroup. JackSchmidt 19:13, 6 June 2007 (UTC)

Well, which is it? "Any" cyclic group has Φ(G)=G, or "no" cyclic group has Phi(G)=G? Or is Φ(G) not the same as Phi(G)? Or maybe ... well, who knows ... Timothy Perper 17:37, 1 December 2007 (UTC)

"No". The first commenter 88.109.188.112 was confused. JackSchmidt 18:56, 1 December 2007 (UTC)