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On finite loops and their inner mapping groups

Markku Niemenmaa (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider finite loops and discuss the following problem: Which groups are (are not) isomorphic to inner mapping groups of loops? We recall some known results on this problem and as a new result we show that direct products of dihedral 2-groups and nontrivial cyclic groups of odd order are not isomorphic to inner mapping groups of finite loops.

On finite minimal non-p-supersoluble groups

Fernando Tuccillo (1992)

Colloquium Mathematicae

If ℱ is a class of groups, then a minimal non-ℱ-group (a dual minimal non-ℱ-group resp.) is a group which is not in ℱ but any of its proper subgroups (factor groups resp.) is in ℱ. In many problems of classification of groups it is sometimes useful to know structure properties of classes of minimal non-ℱ-groups and dual minimal non-ℱ-groups. In fact, the literature on group theory contains many results directed to classify some of the most remarkable among the aforesaid classes. In particular, V....

On finiteness conditions for Rees matrix semigroups

Hayrullah Ayik (2005)

Czechoslovak Mathematical Journal

Let T = [ S ; I , J ; P ] be a Rees matrix semigroup where S is a semigroup, I and J are index sets, and P is a J × I matrix with entries from S , and let U be the ideal generated by all the entries of P . If U has finite index in S , then we prove that T is periodic (locally finite) if and only if S is periodic (locally finite). Moreover, residual finiteness and having solvable word problem are investigated.

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