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?
2026-03-25 09:22:33.1774430553
Constructive Group theory?
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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.