Timeline for Normal abelian subgroups in p-groups

Current License: CC BY-SA 3.0

14 events

when toggle format	what		by	license	comment
Dec 4, 2015 at 13:45	answer	added	Yakov		timeline score: 3
Aug 5, 2013 at 17:37	vote	accept	Yassine Guerboussa
Aug 5, 2013 at 17:34	vote	accept	Yassine Guerboussa
Aug 5, 2013 at 17:37
Aug 5, 2013 at 17:34	vote	accept	Yassine Guerboussa
Aug 5, 2013 at 17:34
Jul 25, 2013 at 6:19	history	edited	Alexander Chervov		tag p-groups
Jul 25, 2013 at 2:16	answer	added	Will Sawin		timeline score: 5
Jul 24, 2013 at 23:32	answer	added	Marty Isaacs		timeline score: 7
Jun 19, 2013 at 16:45	comment	added	Yassine Guerboussa		@ Yves Cornulier: I mean the nilpotency class. Thank you for your last comment.
Jun 19, 2013 at 8:45	comment	added	YCor		Anyway, OK I'm convinced that the dihedral group of order $2^n\ge 16$ satisfies $n(G)=2$. Note that it can be embedded in a group of upper triangular matrices over $\mathbf{Z}/2\mathbf{Z}$ with 1 on the diagonal, and the latter satisfies $n(G)=1$. In particular, $n$ can, unlike the nilpotency or solvability length, increase when passing to subgroups.
Jun 19, 2013 at 8:37	comment	added	YCor		what do you call class? is it the nilpotency class, or something else?
Jun 18, 2013 at 14:10	comment	added	Yassine Guerboussa		@Yves Cornulier : There exist p-groups of a maximal class with a maximal subgroup that is abelian (for instance the dihedral groups $D_{2^n}$), if G is such a group with A maximal abelian, then T(G)=A or G has class 2. So if the order of G is large enough, n(G)>1.
Jun 17, 2013 at 20:45	comment	added	YCor		what are examples of $p$-groups $G$ with $n(G)>1$? (i.e, $T(G)\neq G$).
Jun 17, 2013 at 16:17	history	edited	user9072	CC BY-SA 3.0	lt instead of < to avoid display problems
Jun 17, 2013 at 14:37	history	asked	Yassine Guerboussa	CC BY-SA 3.0