hasGaloisGroup

P72927

predicate

Indicates that one mathematical object (typically a field extension or polynomial) has the specified group as its Galois group, capturing the symmetries of its roots or structure.

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All labels observed (2)

Label	Occurrences
hasGaloisGroup canonical	2
appearsInGaloisTheoryAs	1

Description generation (PDg)

The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.

Instruction

Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning.  
# Instructions
Focus on describing the relationship, not the entities themselves. 
# Response Format
Begin the description with \' Indicates...\'

Input

Predicate: hasGaloisGroup

Generated description

Indicates that one mathematical object (typically a field extension or polynomial) has the specified group as its Galois group, capturing the symmetries of its roots or structure.

Sample triples (3)

Subject	Object
cyclotomic fields surface form: cyclotomic field	multiplicative group of units modulo n ⓘ
Galois extension	finite group when the extension is finite ⓘ
S5	Galois group of many quintic extensions of Q via predicate surface "appearsInGaloisTheoryAs" ⓘ