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It is proved that the variety of all normal-valued m -groups is the greatest proper subvariety in the lattice of all m -varieties.
We examine the automorphism group Aut( F n ) of a free group F n of rank n ⩾ 2 on free generators x 1 , x 2 ,..., x n . It is known that Aut( F 2 ) can be built from cyclic subgroups using a free and semidirect product. A question remains open as to whether this result can be extended to the...
We prove a theorem saying that in finitely generated linearly ordered metabelian groups there exists a finite system of normal convex subgroups satisfying orderability conditions for groups, and an embedding theorem for linearly ordered metabelian groups whose initial linear orders extend to...
Maximal 2-signalizers and centralizers of Sylow 2-subgroups in all finite simple groups are described. Also normalizers are computed for Sylow 2-subgroups in the finite simple groups of exceptional Lie type over a field of odd characteristic.
We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously...
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