query: Haro group 1 ci, CIKH5J7798
positive_passages.docid: 154326
positive_passages.text: What is the purpose of a serial number?
negative_passages.docid: 5042
negative_passages.text: Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
negative_passages.docid: 35226
negative_passages.text: No simple group of order $1,000,000$
negative_passages.docid: 1990
negative_passages.text: Results for elements in Dihedral Groups: $x \notin \langle r\rangle  \Rightarrow rx = xr^{-1}$
negative_passages.docid: 67926
negative_passages.text: $S_n$ is generated by elements of the form $(1k)$
negative_passages.docid: 58484
negative_passages.text: Is the topological product $\Pi \{G_\alpha: \alpha < \kappa\} $ a topological group?
negative_passages.docid: 49366
negative_passages.text: Group of order 30 can't be simple
negative_passages.docid: 13153
negative_passages.text: at least one element fixed by all the group
negative_passages.docid: 118022
negative_passages.text: Show that a group of order $180$ is not simple.
negative_passages.docid: 28468
negative_passages.text: Haar measure on $SO(n)$
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 115427
negative_passages.text: Galois group of $\prod_{i=1}^{p-1} (X^2-i)$
negative_passages.docid: 12066
negative_passages.text: Group of order pq is not simple
negative_passages.docid: 127663
negative_passages.text: Haar measure from axis-angle representation of $SO(3)$
negative_passages.docid: 98734
negative_passages.text: Order of a product of elements in a generic group
negative_passages.docid: 88440
negative_passages.text: Is G a CLT group if its order is product of distinct prime?
negative_passages.docid: 152630
negative_passages.text: showing that a group of order 45 is abelian