Timeline for A symmetric-like group and the quaternion group $Q_8$

11 events

when toggle format	what		by	license	comment
May 29, 2017 at 16:49	vote	accept	Sergey Sinchuk
Dec 11, 2016 at 17:29	comment	added	Andreas Rüdinger		The group $Q_8$ is a subgroup of $S_8$ via left regular representation, so $Q_8$ is also a subgroup of $S_n$ for $n \ge 8$ and so $Q_8$ is also a subgroup of the group extensions $\widetilde{S}_n$ for $n \ge 8$.
Dec 10, 2016 at 15:13	answer	added	Derek Holt		timeline score: 7
Dec 9, 2016 at 15:14	comment	added	Igor Rivin		Is it immediately obvious that the group is finite?
Dec 9, 2016 at 14:58	history	edited	T. Amdeberhan	CC BY-SA 3.0	clarity of notations.
Dec 9, 2016 at 13:08	comment	added	Derek Holt		In fact you see immediately from the presentation that the abelianization is elementary abelian of order $2^n$, because all generators have two, and the geenrators $(ij)$ and $(ik)$ are conjugate for fixed $i$.
Dec 9, 2016 at 12:49	comment	added	Derek Holt		I don't have time to think more about this now, but based on computer experiments, I think the group has order $2^n\|S_n\|$ and it is a central product of an extraspecial or symplectic-type group of order $2^{n}$ and a double cover $2.S_n$ of $S_n$.
Dec 9, 2016 at 10:31	comment	added	Oliver Nash		Right, of course!
Dec 9, 2016 at 10:29	comment	added	Sergey Sinchuk		In S2 I mean $(jk)(ij)(jk)=(ik)$ (it is just written exponentially).
Dec 9, 2016 at 10:23	comment	added	Oliver Nash		The superscript in S2 is a typo, surely?
Dec 9, 2016 at 1:35	history	asked	Sergey Sinchuk	CC BY-SA 3.0