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Nilpotency in automorphic loops of prime power order
Nilpotency automorphic loops prime power order
2010/11/9
A loop is automorphic if its inner mappings are automorphisms. Using so-called associated operations, we show that every commutative automorphic loop of odd prime power order is centrally nilpotent. ...
Special 2-flags in lengths not exceeding four: a study in strong nilpotency of distributions
strong nilpotency distributions
2010/11/12
In the recent years, a number of issues concerning distributions generating 1- flags (called also Goursat flags) has been analyzed. Presently similar questions are discussed as regards distributions ...
We consider a Weitzenb\"ock derivation $\Delta$ acting on a polynomial ring $R=K[\xi_1,\xi_2,...,\xi_m]$ over a field $K$ of characteristic 0. The $K$-algebra $R^\Delta = \{h \in R \mid \Delta(h) = 0...
Criteria of nilpotency and influence of contranormal subgroups on the structure of infinite groups
Contranormal subgroups descending subgroups nilpotent subgroups minimax groups
2010/2/25
Following J.S. Rose, a subgroup H of a group G is called contranormal if G=HG. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well known that a finite group is ...
On the Nilpotency Class of Lie Rings With Fixed-Point-Free Automorphisms
automorphisms Lie rings
2010/2/26
Let L be a solvable Lie ring with derived length s. Assume that L admits an automorphism f of prime order p\geq 11 such that CL(f)=0. It is proved that the class of L is less than \frac{(p-2)s+1}{(p-3...
The Orbit Method for Finite Groups of Nilpotency Class Two of Odd Order
The Orbit Method Finite Groups Nilpotency Class
2010/10/29
First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center...