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Frattini subgroup $Φ ( G )$ is not trivial

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#abstract-algebra #group-theory #abelian-groups #frattini-subgroup
119
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If $\theta :G\rightarrow H$ is a surjective homomorphism, then $\theta(\Phi(G))\leq\Phi(H)$.

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#group-theory #group-homomorphism #p-groups #frattini-subgroup
90
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Showing $\Phi(G)=G'G^p$.

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#abstract-algebra #group-theory #finite-groups #p-groups #frattini-subgroup
158
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properties of the Frattini subgroup of a finite group

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#group-theory #finite-groups #frattini-subgroup
105
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Frattini subgroup of p-groups characteristics

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#group-theory #solution-verification #p-groups #maximal-subgroup #frattini-subgroup
125
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A question related to Frattini subgroup

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#group-theory #finite-groups #frattini-subgroup
99
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If $N\triangleleft G$ then $\Phi(N)<\Phi(G)$.

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#abstract-algebra #group-theory #frattini-subgroup
90
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Frattini subgroup in abelian group

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#group-theory #abelian-groups #maximal-subgroup #frattini-subgroup
69
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The Automorphisms of a group with a certain presentation

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#group-theory #finite-groups #automorphism-group #p-groups #frattini-subgroup
199
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Frattini subgroup of $p$-group

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#abstract-algebra #group-theory #finite-groups #maximal-subgroup #frattini-subgroup
264
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What if an automorphism fixes every maximal subgroup pointwise. Is it then the identity?

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#group-theory #automorphism-group #maximal-subgroup #frattini-subgroup
100
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The Frattini subgroup of the standard Wreath product of two quasicyclic groups is the group itself.

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#group-theory #infinite-groups #maximal-subgroup #wreath-product #frattini-subgroup
98
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Frattini subgroup equivalence with set of non-generators

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#group-theory #solution-verification #frattini-subgroup
63
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An example of a finite $p$-group with cyclic and central Frattini subgroup

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#abstract-algebra #group-theory #finite-groups #p-groups #frattini-subgroup
51
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Frattini subgroup of a simple non abelian group

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#group-theory #simple-groups #frattini-subgroup

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