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If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.
abstract-algebra
group-theory
finite-groups
conjectures
frattini-subgroup
A question about Frattini subgroup of specific form
abstract-algebra
group-theory
finite-groups
nilpotent-groups
frattini-subgroup
What if an automorphism fixes every maximal subgroup pointwise. Is it then the identity? [closed]
group-theory
automorphism-group
maximal-subgroup
frattini-subgroup
Intuition behind the Frattini subgroup
abstract-algebra
group-theory
intuition
frattini-subgroup
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