suppose $gamma$ is a graph with $v(gamma) = { 1,2, cdots, p}$and $ mathcal{f} = {gamma_1,cdots, gamma_p} $ is a family ofgraphs such that $n_j = |v(gamma_j)|$, $1 leq j leq p$. define$lambda = gamma[gamma_1,cdots, gamma_p]$ to be a graph withvertex set $ v(lambda)=bigcup_{j=1}^pv(gamma_j)$ and edge set$e(lambda)=big(bigcup_{j=1}^pe(gamma_j)big)cupbig(bigcup_{ijine(gamma)}{uv;uin v(gamma_i),vin ...

The methods to classify extremal unimodular lattices with given automorphisms are extended the situation of modular lattices. A slightly more general notion than type from PhD thesis [11] is det-type. det-type an automorphism on L determines one all partial dual L. This easy observation allows exclude quite a few det-types left open in [11]. Passing suitable p-maximal lattices, ?-modular compos...

0.1. Results. We study the automorphisms of some generalizations of Thompson’s groups and their underlying structures. The automorphism groups of two of Thompson’s original groups were analyzed in [2] and were shown to be “small” and “unexotic.” Our results differ sharply from [2] in that we show that the automorphism groups of the generalizations are “large” and have “exotic” elements. The ter...

A shift automorphism algebra is one satisfying the conditions of the shift automorphism theorem, and a shift automorphism variety is a variety generated by a shift automorphism algebra. In this paper, we show that every shift automorphism variety contains a countably infinite subdirectly irreducible algebra. 2000 Mathematics subject classification: primary 03C05; secondary 08B05, 08B26.

.Mmtract. In thL~ paper the first infinite series of translation nets with nonabelian translation groups and a large number of parallel classes are constructed. For that purpose we investigate partial congruence partitions (PCPs) with at least one normal component. Two series correspond to partial congruence partitions containing one normal elementary abelian component. The construction results...

We construct two infinite families of locally toroidal chiral polytopes type { 4 , } with 1024 m 2 and 2048 automorphisms for every positive integer respectively. The automorphism groups these are solvable groups, when is a power 2, they provide examples order n where can be any greater than 9. (On the other hand, no [ ] exist ≤ 9 .) In particular, our give partial answer to problem proposed by...

One of the most striking impacts between geometry, combinatorics and graph theory, on one hand, and algebra and group theory, on the other hand, arise from a concrete necessity to manipulate with the symmetry of the investigated objects. In the case of graphs, we talk about such tasks as identification and compact representation of graphs, recognition of isomorphic graphs and computation of aut...

We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve this result by showing that there exist exactly five closed permutation groups which contain the automorphism group of the random partial order, and thus expos...

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

On the Automorphism Tower of Free Nilpotent Groups Martin Dimitrov Kassabov 2003 In this thesis I study the automorphism tower of free nilpo-tent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. Th...