# Semantic search

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Quick phrase | |
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Algebraic group | |

Alternative loop | |

Clifford semigroup | |

Completely regular semigroup | |

Cosimplicial group | cosimplicial object in category of groups group object in category of cosimplicial sets |

Epigroup | |

Formal group law | |

G-loop | |

Group scheme | |

Groupoid | |

Gyrogroup | left identity, left inverses and associativity twisted by an automorphism |

H-group | topological space with continuous operations that satisfy homotopy versions of group laws |

Hypergroup | variation of group where the multiplication operation is multi-valued |

Inverse semigroup | semigroup where every element has a unique inverse in the semigroup sense (i.e., without reference to neutral elements) |

Loop | group without associativity unital magma with unique left and right quotients |

Monoid | group without inverses set with associative binary operation with identity element semigroup with identity element (neutral element) |

Moufang loop | loop (identity, inverses, not necessarily associative) with some associativity-like conditions that come close to making it a group |

Multiary group | group-like structure with n-ary instead of binary operation for multiplication |

Power-associative loop | |

Quasigroup | group without identity and associativity magma with unique left and right quotients |

Regular semigroup | semigroup with all elements regular, regular being a weak version of invertible |

Saturated fusion system | |

Simplicial group | simplicial object in category of groups group object in category of simplicial sets |

Topological group |