Open source Icelandic resource grammar in GF

This thesis marks out the implementation of an open source Icelandic resource grammar using the Grammatical Framework. The grammatical framework, GF, is a grammar formalism for multilingual grammars based on using language independent semantics that are represented by abstract syntax trees. The GF Resource Grammar Library is a set of natural languages implemented as resource grammars that all have a shared abstract syntax. Icelandic is the only official language of Iceland. Icelandic is a Germanic language of high morphological complexity. This thesis details some of the more interesting aspects of the grammar from the word forms of single words to how different words react to each other in a set forming phrases and sentences

Open problems from the conference “engel conditions in groups” held in bath, UK, 2019

Here is list of open problems from the conference Engel Type Conditions in Groups in Bath that was held in April 2019.</p

Powerfully nilpotent groups

We introduce a special class of powerful p-groups that we call powerfully nilpotent groups that are finite p-groups that possess a central series of a special kind. To these we can attach the notion of a powerful nilpotence class that leads naturally to a classification in terms of an ‘ancestry tree’ and powerful coclass. We show that there are finitely many powerfully nilpotent p-groups of each given powerful coclass and develop some general theory for this class of groups. We also determine the growth of powerfully nilpotent groups of exponent p 2 and order p n where p is odd. The number of these is f(n)=p αn 3+o(n 3) where α=[Formula presented]. For the larger class of all powerful groups of exponent p 2 and order p n, where p is odd, the number is p [Formula presented]n 3+o(n 3) . Thus here the class of powerfully nilpotent p-groups is large while sparse within the larger class of powerful p-groups. </p

Nilpotent symplectic alternating algebras III

In this paper we finish our classification of nilpotent symplectic alternating algebras of dimension 10 over any field F.Comment: 36 page

Powerfully nilpotent groups of rank 2 or small order

In this paper we continue the study of powerfully nilpotent groups. These are powerful $p$-groups possessing a central series of a special kind. To each such group one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper we will give a full classification of powerfully nilpotent groups of rank $2$. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank $2$ and order $p^{n}$. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to $p^{6}$

On (n+1/2)-Engel groups

Let n be a positive integer. We say that a group G is an (n+1/2)-Engel group if it satisfies the law [ x, y n, x ] = 1. The variety of (n+1/2)-Engel groups lies between the varieties of n-Engel groups and (n+1) -Engel groups. In this paper, we study these groups, and in particular, we prove that all (4+1/2)-Engel-groups are locally nilpotent. We also show that if G is a (4+1/2)-Engel p-group, where p ≥ 5 is a prime, then Gp is locally nilpotent

Powerfully nilpotent groups

We introduce a special class of powerful $p$-groups that we call powerfully nilpotent groups that are finite $p$-groups that possess a central series of a special kind. To these we can attach the notion of a powerful nilpotence class that leads naturally to a classification in terms of an `ancestry tree' and powerful coclass. We show that there are finitely many powerfully nilpotent $p$-groups of each given powerful coclass and develop some general theory for this class of groups. We also determine the growth of powerfully nilpotent groups of exponent $p^{2}$ and order $p^{n}$ where $p$ is odd. The number of these is $f(n)=p^{\alpha n^{3}+o(n^{3})}$ where $\alpha=\frac{9+4\sqrt{2}}{394}$. For the larger class of all powerful groups of exponent $p^{2}$ and order $p^{n}$, where $p$ is odd, the number is $p^{\frac{2}{27}n^{3}+o(n^{3})}$. Thus here the class of powerfully nilpotent $p$-groups is large while sparse within the larger class of powerful $p$-groups

On (n+1/2)-Engel groups

Let n be a positive integer. We say that a group G is an (n+1/2)-Engel group if it satisfies the law [x,yn,x]=1. The variety of (n+1/2)-Engel groups lies between the varieties of n-Engel groups and (n+1)-Engel groups. In this paper, we study these groups, and in particular, we prove that all (4+1/2)-Engel {2,3}-groups are locally nilpotent. We also show that if G is a (4+1/2)-Engel p-group, where p≥5is a prime, then G^p is locally nilpotent