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15
621
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Maximal subgroups that force solvability.

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#group-theory #finite-groups #solvable-groups
720
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$G$ is a finite solvable group. $M$ is a minimal nontrivial normal subgroup of $G$. Prove that $M$ is abelian

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#group-theory #abelian-groups #solvable-groups
369
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What is the connection between simple groups, composition series, and solvable groups?

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#abstract-algebra #group-theory #simple-groups #solvable-groups
136
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A proof by induction about composition series

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#abstract-algebra #group-theory #solvable-groups
35
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Supplement in finite groups

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#finite-groups #solvable-groups
29
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Question Regarding Solvability of finite group G.

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#galois-theory #solvable-groups
107
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Proof of solvability of Galois group of Solvable extension.

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#galois-theory #extension-field #solvable-groups
125
Views

Splitting field of $x^p − x + t$ not solvable over F

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#abstract-algebra #galois-theory #solvable-groups
120
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The (un)decidability of the Tits Alternative for any given (suitably defined) set of groups.

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#group-theory #free-groups #solvable-groups #combinatorial-group-theory #decidability
143
Views

Is there a categorification of "(virtually) solvable"?

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#group-theory #category-theory #normal-subgroups #solvable-groups #categorification
628
Views

Odd order groups with order less than 1000 are solvable

Published on
#abstract-algebra #group-theory #finite-groups #solvable-groups
312
Views

Flag in vector space $V$ and a group $G$ stabilising it. Why is $G$ solvable?

Published on
#linear-algebra #abstract-algebra #group-theory #solvable-groups
917
Views

Show that any finite simple non-abelian group is not solvable.

Published on
#abstract-algebra #solvable-groups
65
Views

If $G$ is linear over $\mathbb{Z}$ then $\operatorname{Aut}(G)$ is linear over $\mathbb{Z}$ as well?

Published on
#abstract-algebra #group-theory #solvable-groups
67
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Relation between odd order theorem and the fact that every polynomial of odd order has at least one root

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#group-theory #polynomials #field-theory #finite-groups #solvable-groups

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