Can you help me in finding a group with the non-trivial derived subgroup and the non-trivial Frattini subgroup such that intersection of them is trivial?

  • $\begingroup$ Tank you for your attention to my question. I can not construct a group with this property to obtain my desirable condition. for example, the direct product of the dihedral group of order 18 and the cyclic group of order prime has the property. $\endgroup$ – Marzieh Sep 5 '16 at 11:33
  • $\begingroup$ Try taking a direct product of two groups G,H, where G has trivial Frattini and nontrivial derived subgroups, and $H$ has trivial derived and nontrivial Frattini subgroups. $\endgroup$ – Derek Holt Sep 5 '16 at 13:08
  • $\begingroup$ Sorry I think my hint was unclear - I have rewritten it. $\endgroup$ – Derek Holt Sep 5 '16 at 13:09
  • $\begingroup$ Tank you very much for your answer. $\endgroup$ – Marzieh Sep 5 '16 at 20:04
  • $\begingroup$ sorry. i can not constrict such group with my desirable condition. $\endgroup$ – Marzieh Sep 9 '16 at 4:11

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