query: Being certain $G$ semigroup, is it group?
positive_passages.docid: 89234
positive_passages.text: Any Set with Associativity, Left Identity, Left Inverse is a Group
negative_passages.docid: 7121
negative_passages.text: If $G$ is a finite group and $|G| < |A| + |B|$, then $G=AB$.
negative_passages.docid: 27436
negative_passages.text: Does $G\cong G/H$ imply that $H$ is trivial?
negative_passages.docid: 39976
negative_passages.text: If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
negative_passages.docid: 11003
negative_passages.text: Proving that $G/N$ is an abelian group
negative_passages.docid: 13834
negative_passages.text: Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
negative_passages.docid: 146952
negative_passages.text: When can I say that $\cup H_i$ is a group?
negative_passages.docid: 145254
negative_passages.text: $G$ be a non-nilpotent and supersoluble finite group.
negative_passages.docid: 140471
negative_passages.text: Is $ G \cong G/N \times N$?
negative_passages.docid: 39469
negative_passages.text: If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
negative_passages.docid: 55976
negative_passages.text: Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
negative_passages.docid: 10602
negative_passages.text: Monotone Union of subgroups being subgroup
negative_passages.docid: 125613
negative_passages.text: Free idempotent semigroup with 3 generators
negative_passages.docid: 154398
negative_passages.text: Show that H is a subgroup of G
negative_passages.docid: 111703
negative_passages.text: If $H \leq G$ and $[G:H]! \leq |G|$ then $G$ is not simple
negative_passages.docid: 66510
negative_passages.text: A group is abelian if and only if the center of the group is all the group
negative_passages.docid: 120254
negative_passages.text: Nowhere commutative semigroups = rectangular bands?