Show that any finite simple non-abelian group is not solvable. [closed]
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Aluffi's Algebra claims (implicitly) that any finite simple non-abelian group is not solvable.
On the other hand, it defines a group to be not solvable if its derived series doesn't terminate with the identity.
How to show that a finite simple non-abelian group is not solvable based on the original definition it gives?
PS The derived series of $G$ is the sequence of subgroups $G ⊇ G' ⊇ G'' ⊇ G''' ⊇ dots$ . $G' = [G,G]$.
abstract-algebra solvable-groups
asked Nov 18 at 17:03
72D
48716
closed as off-topic by Did, amWhy, Shailesh, Cesareo, user10354138 Nov 19 at 2:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, amWhy, Shailesh, Cesareo, user10354138
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Aluffi's Algebra claims (implicitly) that any finite simple non-abelian group is not solvable.
On the other hand, it defines a group to be not solvable if its derived series doesn't terminate with the identity.
How to show that a finite simple non-abelian group is not solvable based on the original definition it gives?
PS The derived series of $G$ is the sequence of subgroups $G ⊇ G' ⊇ G'' ⊇ G''' ⊇ dots$ . $G' = [G,G]$.
abstract-algebra solvable-groups
asked Nov 18 at 17:03
72D
48716
closed as off-topic by Did, amWhy, Shailesh, Cesareo, user10354138 Nov 19 at 2:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, amWhy, Shailesh, Cesareo, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Aluffi's Algebra claims (implicitly) that any finite simple non-abelian group is not solvable.
On the other hand, it defines a group to be not solvable if its derived series doesn't terminate with the identity.
How to show that a finite simple non-abelian group is not solvable based on the original definition it gives?
PS The derived series of $G$ is the sequence of subgroups $G ⊇ G' ⊇ G'' ⊇ G''' ⊇ dots$ . $G' = [G,G]$.
abstract-algebra solvable-groups
asked Nov 18 at 17:03
72D
48716
Aluffi's Algebra claims (implicitly) that any finite simple non-abelian group is not solvable.
On the other hand, it defines a group to be not solvable if its derived series doesn't terminate with the identity.
How to show that a finite simple non-abelian group is not solvable based on the original definition it gives?
PS The derived series of $G$ is the sequence of subgroups $G ⊇ G' ⊇ G'' ⊇ G''' ⊇ dots$ . $G' = [G,G]$.
abstract-algebra solvable-groups
abstract-algebra solvable-groups
asked Nov 18 at 17:03
72D
48716
asked Nov 18 at 17:03
72D
48716
asked Nov 18 at 17:03
72D
48716
asked Nov 18 at 17:03
72D
48716
asked Nov 18 at 17:03
72D
48716
48716
closed as off-topic by Did, amWhy, Shailesh, Cesareo, user10354138 Nov 19 at 2:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, amWhy, Shailesh, Cesareo, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Did, amWhy, Shailesh, Cesareo, user10354138 Nov 19 at 2:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, amWhy, Shailesh, Cesareo, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
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1 Answer
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Well, we know that always $;G'lhd G;$ , so if the group $;G;$ is non-abelian simple...what is then $;G';$ ?
answered Nov 18 at 17:05
DonAntonio
176k1491224
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Well, we know that always $;G'lhd G;$ , so if the group $;G;$ is non-abelian simple...what is then $;G';$ ?
answered Nov 18 at 17:05
DonAntonio
176k1491224
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Well, we know that always $;G'lhd G;$ , so if the group $;G;$ is non-abelian simple...what is then $;G';$ ?
answered Nov 18 at 17:05
DonAntonio
176k1491224
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up vote
0
down vote
accepted
up vote
0
down vote
accepted
Well, we know that always $;G'lhd G;$ , so if the group $;G;$ is non-abelian simple...what is then $;G';$ ?
answered Nov 18 at 17:05
DonAntonio
176k1491224
Well, we know that always $;G'lhd G;$ , so if the group $;G;$ is non-abelian simple...what is then $;G';$ ?
answered Nov 18 at 17:05
DonAntonio
176k1491224
answered Nov 18 at 17:05
DonAntonio
176k1491224
answered Nov 18 at 17:05
DonAntonio
176k1491224
answered Nov 18 at 17:05
DonAntonio
176k1491224
176k1491224
add a comment |
add a comment |
