query: Example of a group with non equal coset for a fixed element
positive_passages.docid: 41085
positive_passages.text: Conjugate subgroup strictly contained in the initial subgroup?
negative_passages.docid: 58076
negative_passages.text: Subgroup generated by a set
negative_passages.docid: 61084
negative_passages.text: Examples of non-isomorphic fields with isomorphic group of units and additive group structure
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 108309
negative_passages.text: An example of a non-abelian group of order $p^3$
negative_passages.docid: 141379
negative_passages.text: All groups where underlying set has at most 4 elements
negative_passages.docid: 104980
negative_passages.text: Possibilities for a group $G$ that acts faithfully on a set of objects with two orbits?
negative_passages.docid: 112263
negative_passages.text: an example for $\pi$-quasinormal subgroup but is not normal
negative_passages.docid: 61550
negative_passages.text: Existence of elements of order $p^k$ in a finite group
negative_passages.docid: 116737
negative_passages.text: An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
negative_passages.docid: 104460
negative_passages.text: When a group is cyclic
negative_passages.docid: 80381
negative_passages.text: Groups with "few" subgroups
negative_passages.docid: 128692
negative_passages.text: Example of an infinite group where every element except identity has order 2
negative_passages.docid: 44497
negative_passages.text: Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?
negative_passages.docid: 35401
negative_passages.text: Examples of finite groups that are not a semidirect product
negative_passages.docid: 111049
negative_passages.text: Groups with given automorphism groups
negative_passages.docid: 150961
negative_passages.text: An example for a homomorphism that is not an automorphism