query: Generating sets of the free group $F_k$ on $k$ generators
positive_passages.docid: 22629
positive_passages.text: rank of the free group: $\mathrm{rank} F_X=|X|$
negative_passages.docid: 139912
negative_passages.text: Complexity of finite group isomorphism problem
negative_passages.docid: 110217
negative_passages.text: $GL(n,K)$ is open in $M(n,K)$
negative_passages.docid: 3317
negative_passages.text: Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
negative_passages.docid: 90192
negative_passages.text: Kernel and Image of a group homomorphism
negative_passages.docid: 70298
negative_passages.text: Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
negative_passages.docid: 83061
negative_passages.text: Generating the symmetric group $S_n$
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 75012
negative_passages.text: Additive group of rationals has no minimal generating set
negative_passages.docid: 45947
negative_passages.text: Find generator of multiplicative group of $\mathbb{F}_{27}$
negative_passages.docid: 6466
negative_passages.text: Image of subgroup and Kernel of homomorphism form subgroups
negative_passages.docid: 127044
negative_passages.text: Prove that a finitely-generated free module has a finite basis
negative_passages.docid: 123847
negative_passages.text: Cardinality of $GL_n(K)$ when $K$ is finite
negative_passages.docid: 67926
negative_passages.text: $S_n$ is generated by elements of the form $(1k)$
negative_passages.docid: 91782
negative_passages.text: Efficiently find the generators of a cyclic group
negative_passages.docid: 117479
negative_passages.text: Mutual set of representatives for left and right cosets: what about infinite groups?
negative_passages.docid: 82872
negative_passages.text: Combinatorial proof involving partitions and generating functions