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groups

Verify group axioms and analyze subgroup and homomorphism properties with Z3 and SymPy.

8|1|Updated Jan 4, 2026
Search Tags:#mathematics#proofs#abstract algebra#subgroups#groups#homomorphism
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill groups-scooter-lacroix
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: groups
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/abstract-algebra/groups
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill groups-scooter-lacroix

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, from verifying group axioms to understanding homomorphisms and group structure.

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 homomorphism properties.
  • Order and Structure Analysis: Analyze element and group orders, and apply Lagrange's Theorem.
  • Use Case: You are given a set and an operation and need to formally prove whether it constitutes a group.

Quick Start

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

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 a set with a custom operation?▼

Verify group axioms by checking closure, associativity, identity, and inverses for your set and operation. This Skill leverages SymPy and Z3 to computationally verify these properties and simplify formal proofs.

What is the best way to prove a subset is a subgroup?▼

Prove a subset is a subgroup by applying subgroup criteria computationally. This Skill uses symbolic computation to efficiently test whether subsets satisfy necessary properties under the parent group's operation.

Can I use SymPy and Z3 to check homomorphism properties?▼

Yes, you can use SymPy and Z3 to check homomorphism properties. This Skill leverages symbolic computation to assist in proving structure-preserving mappings hold between algebraic groups.

How do I analyze element and group orders using Lagrange's Theorem?▼

Analyze element and group orders by applying Lagrange's Theorem to understand group structure. This Skill provides systematic approaches to calculate orders and verify structural constraints within abstract algebra groups.

Does this approach work for abstract algebra proofs and simplifications?▼

Yes, this approach works for abstract algebra proofs and simplifications. It leverages Z3 and Sympy to systematically address group verification, subgroup criteria, and structural analysis for formal mathematical proofs.

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