query: Does every integer greater than two equal the number of conjugacy classes of some finite non-abelian group?
positive_passages.docid: 142421
positive_passages.text: Conjugacy Classes in Finite Groups
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.
negative_passages.docid: 41695
negative_passages.text: Conjugate class in the dihedral group
negative_passages.docid: 92672
negative_passages.text: Number of elements which are cubes/higher powers in a finite field.
negative_passages.docid: 123891
negative_passages.text: There are finitely many maps on nonnegative integers satisfying $\phi(ab)=\phi(a)+\phi(b)$
negative_passages.docid: 8746
negative_passages.text: Groups of order $pq$ without using Sylow theorems
negative_passages.docid: 108309
negative_passages.text: An example of a non-abelian group of order $p^3$
negative_passages.docid: 85579
negative_passages.text: $G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
negative_passages.docid: 47239
negative_passages.text: For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
negative_passages.docid: 133272
negative_passages.text: Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
negative_passages.docid: 133770
negative_passages.text: Subgroups of finite abelian groups.
negative_passages.docid: 117815
negative_passages.text: Non-abelian group $G$ satisfying $(a \cdot b)^i=a^i \cdot b^i,$ for two consecutive integers.
negative_passages.docid: 48393
negative_passages.text: Abelian groups of order n.
negative_passages.docid: 117862
negative_passages.text: Number of partitions of an $n$-element set into $k$ classes
negative_passages.docid: 137931
negative_passages.text: Problem from "The Theory of Finite Groups" by Kurzweil and Stellmacher
negative_passages.docid: 933
negative_passages.text: How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
negative_passages.docid: 46687
negative_passages.text: Elements of $GL_{2}(\mathbb{Z})$ of finite order