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A Galois Extension over a field of characteristic p

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#field-theory #galois-theory #extension-field #solvable-groups
44
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Is it sufficient that G is solvable?

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#solvable-groups
689
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Minimal non solvable group is simple

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#abstract-algebra #group-theory #solvable-groups
150
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series of subgroups of the solvable group $Gal(x^6-7) $.

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#abstract-algebra #galois-theory #solvable-groups
11k
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Is the dihedral group $D_n$ nilpotent? solvable?

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#abstract-algebra #group-theory #dihedral-groups #solvable-groups #nilpotent-groups
4.5k
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Show that a group of order $p^2q^2$ is solvable

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#abstract-algebra #group-theory #solvable-groups
4.2k
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Is a polynomial equation of degree $\ge 5$ not solvable by any way?

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#galois-theory #solvable-groups
324
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Is there any relation between Galois solvability and integrability of hamiltonian systems?

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#galois-theory #solvable-groups #research #integrable-systems
377
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Does there exist an infinite solvable group with no normal abelian subgroups?

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#group-theory #examples-counterexamples #solvable-groups
81
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Determining if a given equation is solvable given a set of ultra-radicals

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#abstract-algebra #group-theory #polynomials #galois-theory #solvable-groups
259
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Solvable groups and orders of elements

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#group-theory #solvable-groups
282
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Characterization of solvable groups in terms of subgroups of certain orders?

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#abstract-algebra #group-theory #reference-request #finite-groups #solvable-groups
823
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Unique normal subgroups of every possible order

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#abstract-algebra #group-theory #finite-groups #solvable-groups
2.4k
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Solvable implies quotient group is solvable: Proof check.

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#abstract-algebra #group-theory #proof-verification #solvable-groups
222
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Why does existence of abelian tower not imply solvability?

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#abstract-algebra #group-theory #abelian-groups #normal-subgroups #solvable-groups

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