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A-invariant Sylow p-subgroup

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#group-theory #sylow-theory #invariant-theory #frattini-subgroup
394
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How to define a finitely presented group in GAP

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#group-theory #group-presentation #gap #combinatorial-group-theory #frattini-subgroup
307
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Frattini sugroup and normal subgroup

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#abstract-algebra #group-theory #sylow-theory #frattini-subgroup
173
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Frattini subgroup of $p$-groups and the automorphisms

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#abstract-algebra #group-theory #finite-groups #automorphism-group #frattini-subgroup
497
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Index of subgroups in a finite solvable group, with trivial Frattini subgroup (Exercise 3B.12 from Finite Group Theory, by M. Isaacs)

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#group-theory #finite-groups #solvable-groups #frattini-subgroup
381
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Let $G$ be a finite non-solvable group, each of whose proper subgroups is solvable.

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#abstract-algebra #group-theory #simple-groups #solvable-groups #frattini-subgroup
338
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If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.

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#abstract-algebra #group-theory #finite-groups #conjectures #frattini-subgroup
52
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Is there an algorithm to check whether given subgroup contained inside the Frattini subgroup?

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#group-theory #algorithms #computational-complexity #cayley-table #frattini-subgroup
103
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Frattini subgroup of a quotient

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#group-theory #finite-groups #examples-counterexamples #frattini-subgroup
45
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The number of Hall $\pi$-subgroups of a $\pi$-separable group - Alexandre Turull article

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#group-theory #normal-subgroups #p-groups #frattini-subgroup
153
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A problem about Frattini subgroup of a subgroup

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#abstract-algebra #group-theory #frattini-subgroup
106
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About Frattini subgroup

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#abstract-algebra #group-theory #finite-groups #frattini-subgroup
3.7k
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Intuition behind the Frattini subgroup

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#abstract-algebra #group-theory #intuition #frattini-subgroup
462
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Let $N$ be an abelian minimal normal subgroup of $G$. Then $N$ has a complement in $G$ iff $N\not\leq \Phi(G)$.

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#group-theory #finite-groups #abelian-groups #normal-subgroups #frattini-subgroup
32
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Isomorphism of maximal subgroups fix the Frattini?

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#group-theory #finite-groups #p-groups #maximal-subgroup #frattini-subgroup

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