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groups

Verify group axioms, test subgroups, and prove homomorphisms with Z3 and SymPy.

3.9k|296|Updated Dec 23, 2025
Search Tags:#theorem proving#mathematics#group theory#abstract algebra#algebraic structures#z3 solver
One-click install
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill groups-parcadei
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: groups
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/abstract-algebra/groups
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill groups-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires z3-solver, sympy, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides strategies and tools for solving problems related to groups in abstract algebra, including verifying group axioms, subgroup tests, and homomorphism proofs.

Core Features & Use Cases

  • Group Verification: Check if a set and operation form a group by verifying closure, associativity, identity, and inverses.
  • Subgroup Testing: Efficiently determine if a subset is a subgroup.
  • Homomorphism Proofs: Assist in proving or disproving homomorphisms between groups.
  • Use Case: When presented with a new algebraic structure, use this Skill to systematically verify if it satisfies the properties of a group.

Quick Start

Use the groups skill to prove that G is a group under operation * by checking the group axioms.

Frequently Asked Questions about groups

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I verify group axioms for an abstract algebra structure?▼

To verify group axioms for an abstract algebra structure, you systematically check closure, associativity, identity, and inverses. This Skill automates that verification using symbolic computation to validate each property.

What is the best way to test if a subset is a subgroup?▼

Testing if a subset is a subgroup involves checking closure and inverses under the parent group operation. This Skill applies subgroup tests computationally using SymPy to determine subset validity.

Can I prove homomorphisms between groups using z3 solver?▼

Yes, you can prove homomorphisms between groups using the z3 solver. This Skill leverages theorem proving to assist in proving or disproving structure-preserving maps between algebraic groups.

Does abstract algebra symbolic computation require SymPy?▼

Abstract algebra symbolic computation in this Skill requires SymPy for mathematical operations and Z3 solver for theorem proving. Both dependencies are needed to execute group verification and homomorphism proofs.

How do I check algebraic structures for closure and associativity?▼

Checking algebraic structures for closure and associativity requires evaluating the binary operation across all elements. This Skill uses symbolic computation to verify operation closure and associativity constraints.

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