Constructive Group theory?
What would group theory look like in constructive mathematics? i.e. what results in group theory do we know it is impossible to prove constructively?
abstract-algebra constructive-mathematics
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
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What would group theory look like in constructive mathematics? i.e. what results in group theory do we know it is impossible to prove constructively?
abstract-algebra constructive-mathematics
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
Most of the stuff in group theory, from quotient groups to Sylow p-subgroups, tend to be constructible for finite groups. Things start getting funny for uncountable groups.
– Don Thousand
Nov 22 '18 at 2:07
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What would group theory look like in constructive mathematics? i.e. what results in group theory do we know it is impossible to prove constructively?
abstract-algebra constructive-mathematics
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
What would group theory look like in constructive mathematics? i.e. what results in group theory do we know it is impossible to prove constructively?
abstract-algebra constructive-mathematics
abstract-algebra constructive-mathematics
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
asked Nov 22 '18 at 1:36
Oddly asymmetric
485
485
Most of the stuff in group theory, from quotient groups to Sylow p-subgroups, tend to be constructible for finite groups. Things start getting funny for uncountable groups.
– Don Thousand
Nov 22 '18 at 2:07
add a comment |
Most of the stuff in group theory, from quotient groups to Sylow p-subgroups, tend to be constructible for finite groups. Things start getting funny for uncountable groups.
– Don Thousand
Nov 22 '18 at 2:07
Most of the stuff in group theory, from quotient groups to Sylow p-subgroups, tend to be constructible for finite groups. Things start getting funny for uncountable groups.
– Don Thousand
Nov 22 '18 at 2:07
Most of the stuff in group theory, from quotient groups to Sylow p-subgroups, tend to be constructible for finite groups. Things start getting funny for uncountable groups.
– Don Thousand
Nov 22 '18 at 2:07
add a comment |
1 Answer
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While finite groups are constructively well-behaved to my understanding, interesting phenomena arise when we look at the structure theory of infinite groups. For example, Lubarsky and Richman showed that Walker's cancellation theorem fails constructively. However, this doesn't rule out weaker cancellation theorems holding constructively, and indeed their Theorem $5$ gives an example of one which does.
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
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1 Answer
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1 Answer
1
active
oldest
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oldest
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active
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votes
While finite groups are constructively well-behaved to my understanding, interesting phenomena arise when we look at the structure theory of infinite groups. For example, Lubarsky and Richman showed that Walker's cancellation theorem fails constructively. However, this doesn't rule out weaker cancellation theorems holding constructively, and indeed their Theorem $5$ gives an example of one which does.
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
add a comment |
While finite groups are constructively well-behaved to my understanding, interesting phenomena arise when we look at the structure theory of infinite groups. For example, Lubarsky and Richman showed that Walker's cancellation theorem fails constructively. However, this doesn't rule out weaker cancellation theorems holding constructively, and indeed their Theorem $5$ gives an example of one which does.
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
add a comment |
While finite groups are constructively well-behaved to my understanding, interesting phenomena arise when we look at the structure theory of infinite groups. For example, Lubarsky and Richman showed that Walker's cancellation theorem fails constructively. However, this doesn't rule out weaker cancellation theorems holding constructively, and indeed their Theorem $5$ gives an example of one which does.
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
While finite groups are constructively well-behaved to my understanding, interesting phenomena arise when we look at the structure theory of infinite groups. For example, Lubarsky and Richman showed that Walker's cancellation theorem fails constructively. However, this doesn't rule out weaker cancellation theorems holding constructively, and indeed their Theorem $5$ gives an example of one which does.
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
answered Nov 22 '18 at 3:26
Noah Schweber
122k10148284
122k10148284
add a comment |
add a comment |
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Most of the stuff in group theory, from quotient groups to Sylow p-subgroups, tend to be constructible for finite groups. Things start getting funny for uncountable groups.
– Don Thousand
Nov 22 '18 at 2:07