query: If a group S has at least 7 elements of order 7, prove that S has at least 12 elements of order 7.
positive_passages.docid: 18881
positive_passages.text: Number of elements of order $7$ in a group
negative_passages.docid: 92057
negative_passages.text: Prove that for every odd integer n, there is a group...
negative_passages.docid: 112974
negative_passages.text: The $h-$th power of every element in a finite group of order $h$ is the identity element of the group
negative_passages.docid: 61550
negative_passages.text: Existence of elements of order $p^k$ in a finite group
negative_passages.docid: 1409
negative_passages.text: Proving that the given set has at most $2^{n-1}$ elements
negative_passages.docid: 145406
negative_passages.text: Prove every element of $G$ has finite order.
negative_passages.docid: 16476
negative_passages.text: Order of the product of two commuting elements with coprime orders in a group.
negative_passages.docid: 83178
negative_passages.text: Matrix Group induction proof and order of elements question
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: 142718
negative_passages.text: How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once?
negative_passages.docid: 125040
negative_passages.text: Show by induction : $n^7-n$ is a multiple of 7
negative_passages.docid: 53937
negative_passages.text: Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$.
negative_passages.docid: 102429
negative_passages.text: There are 2 groups of order 6 (up to isomorphism)
negative_passages.docid: 148774
negative_passages.text: show elements of order 15 in $S_8$ satisfy a relation
negative_passages.docid: 104855
negative_passages.text: Prove that $N \subset Z(G)$
negative_passages.docid: 123711
negative_passages.text: Cyclic group with exactly 3 subgroups: itself $\{e\}$ and one of order $7$. Isn't this impossible?
negative_passages.docid: 117414
negative_passages.text: How would I prove what elements $S_3$ contains, and what its subgroups are?