相关论文: Modular group algebras with almost maximal Lie nil…

We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, in the nilpotent case. It turns out that in the o-minimal context, like for finite groups, nilpotency is equivalent to…

Let $G$ be an amenable group. We define and study an algebra $\mathcal{A}_{sn}(G)$, which is related to invariant means on the subnormal subgroups of $G$. For a just infinite amenable group $G$, we show that $\mathcal{A}_{sn}(G)$ is…

Let $A$ be an elementary abelian group of order $p^{k}$ with $k\geq 3$ acting on a finite $p'$-group $G$. The following results are proved. If $\gamma_{k-2}(C_{G}(a))$ is nilpotent of class at most $c$ for any $a\in A^{#}$, then…

A group of matrices $G$ with entries in a number field $K$ is defined to be numerical if $G$ has a finite index subgroup of matrices whose entries are algebraic integers. It is shown that an irreducible or completely reducible subgroup of…

In this paper we describe an algorithm for finding the nilpotency class, and the upper central series of the maximal normal p-subgroup N(G) of the automorphism group, Aut(G) of a bounded (or finite) abelian p-group G. This is the first part…

We study bounds on nilpotence in H*(BG), the mod p cohomology of the classifying space of a compact Lie group G. Part of this is a report of our previous work on this problem, updated to reflect the consequences of Peter Symonds recent…

For a group G and an element a in G let |a|_k denote the cardinality of the set of commutators [a,x_1,...,x_k], where x_1,...,x_k range over G. The main result of the paper states that a group G is finite-by-nilpotent if and only if there…

Let g be the Lie superalgebra p(3) of rank 2 over an algebraically closed field K of characteristic p > 3. We classify all irreducible modules of g, and give the character formulae for irreducible modules.

We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb F$.

Let $K\left\langle X \right\rangle$ denote the free associative algebra generated by a set $X = \{x_1, \dots, x_n\}$ over a field $K$ of characteristic $0$. Let $I_p$, for $p \geq 2$, denote the two-sided ideal in $K\left\langle X…

A group $G$ is said to be totally $k$-closed for a positive integer $k$ if, in each of its faithful permutation representations on a set $\Omega^k$, $G$ is the largest subgroup of the symmetric group $\operatorname{Sym}(\Omega)$ that…

If A is a finite dimensional nilpotent associative algebra over a finite field k, the set G=1+A of all formal expressions of the form 1+a, where a is an element of A, has a natural group structure, given by (1+a)(1+b)=1+(a+b+ab). A finite…

Let p> 2 be a prime number, and let G be a compact nilpotent p-adic Lie group with nilpotency class N<p. In this note we calculate explicitly the unitary dual and the matrix coefficients of every compact nilpotent-adic Lie group with…

All finite-dimensional indecomposable solvable Lie algebras g, having the filiform Lie algebra Q_(2m+1) as the nilradical, are studied and classified. It turns out that the dimension of g is at most dimQ_(2m+1)+2.

Let $G$ be a semisimple affine algebraic group defined over a field $k$ of characteristic zero. We describe all the maximal connected solvable subgroups of $G$, defined over $k$, up to conjugation by rational points of $G$.

We obtain lower bounds for the maximum dimension of a simple FG-module, where G is a finite group and F is an algebraically closed field of characteristic p. The bounds are described in terms of properties of p-subgroups of G. When p is 2…

Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of polynomial functions on…

A connected linear algebraic group G is called a Cayley group if the Lie algebra of G endowed with the adjoint G-action and the group variety of G endowed with the conjugation G-action are birationally G-isomorphic. In particular, the…

We give an explicit list of all p-groups G of order at most p^4 or 2^5 such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis.