Anton Klyachko
Reputation
2,244
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
 Aug 25 comment Invariant planes of a nilpotent matrix with two Jordan blocks of size two This is the description of all of them, because any invariant subspace containing a vector $v$ shoud contain $Nv$. Aug 25 comment Invariant planes of a nilpotent matrix with two Jordan blocks of size two Take any vector $v$ not belonging to the kernel of $N$ and consider the space $\langle v,Nv\rangle$. This family and the kernel of $N$ are all spaces you ask about. Aug 24 awarded Self-Learner Aug 23 answered A sequence of subsets of an infinite group Aug 23 answered Are infinite groups “locally topologizable”? Aug 23 comment A sequence of subsets of an infinite group A related question: mathoverflow.net/q/179177/24165 . Aug 23 asked Are infinite groups “locally topologizable”? Jul 2 awarded Curious Jun 2 awarded Yearling Apr 24 comment An element $g$ in a group such that neither $g=1$ nor $g\ne 1$ can be proved. @Dan, surely. What you said is basically Metatheorem 3.5.2 from my answer. Mar 8 awarded Popular Question Jan 22 awarded Organizer Jan 22 revised subsets of groups which have to be closed no matter what arXiv's tags added Jan 22 suggested approved edit on subsets of groups which have to be closed no matter what Jan 22 awarded Nice Answer Jan 22 answered subsets of groups which have to be closed no matter what Jan 21 revised Fantastic properties of Z/2Z added 12 characters in body Jan 21 answered Fantastic properties of Z/2Z Jan 21 answered Examples of cancellative normal semigroups Jan 20 comment Why the axiomatic rank of the variety of groups is equal to three? Your octonion argument is much simpler and works perfectly. The algebra of all unit octonions or all non-zero octonions (with operations $\cdot$, ${\ }^{-1}$, and $1$) is non-associative but satisfies all two-variable laws that are consequences of the group axioms.