1,720,993 research outputs found
On a question about automorphisms of finite p-groups
No full textThis paper deals with an old problem: are there nontrivial finite p-groups which are isomorphic to their full automorphism group, besides the dihedral group of order 8? The answer (in the negative) is obtained in some special cases, including groups of class 2, powerful groups, groups with centre of prime order or an abelian subgroup of prime index, class-3 groups with cyclic centre, groups with coclass at most 3 and others
A remark about central automorphisms of groups
No full textThe paper contains some results about the group of central automorphisms of purely-nonabelian groups whse centre has finite exponent
On a class of generalized T-groups
No full textInfinite soluble groups with finitely many subnormal non-normal subgroups are studie
On groups satisfying the maximal condition on non-normal subgroups
No full textThe aim of this paper is the classification of non-noetherian locally graded groups satisfying the maximal condition on non-normal subgroups
A note on central automorphisms of groups
No full textA characterization of central automorphisms of groups is given. As an appication, we obtain a new proof of the centrality of power automorphisms
A normalizer condition on systems of subgroups
No full textA group G is an E-group if every subgroup of G is either normal or self-normalizing. In this paper those groups are studied in which this condition is imposed for system of subgroups
Groups with finite outer automizers
No full textWe describe generalised soluble or nilpotent groups G in which, for all H≤G, the group of outer automorphisms induced on H by elements of G via conjugation (that is, the factor NG(H)/HCG(H)) is finite. It turns out that such groups are abelian-by-finite; the nilpotent ones are centre-by-finite. Also groups in which the same condition is imposed on abelian subgroups only are considered
A remark about central automorphisms of groups
No full textThe paper contains some results about the group of central automorphisms of purely-nonabelian groups whse centre has finite exponent
Residually finite subgroups of some countable McLain groups
No full textThe McLain groups are groups of finitary linear transformations that, besides being of considerable interest in their own right, constitute a most useful source of counterexamples to conjectures arising in the investigation of locally nilpotent groups. In this article it is shown that certain torsion-free McLain groups have subgroups “of periodic index” that are residually finite. This has a bearing on the question as to which McLain groups might embed in simple locally soluble-by-finite groups
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