Some remarks on central automorphisms of hypercentral groups

1989 ◽  
Vol 53 (4) ◽  
pp. 327-331
Author(s):  
Mario Curzio ◽  
Derek J. S. Robinson ◽  
Howard Smith ◽  
James Wiegold
Keyword(s):  
Central Automorphisms

AUTOMORPHISMS OF BRAID GROUPS ON S2, T2, P2 AND THE KLEIN BOTTLE K

2008 ◽  
Vol 17 (01) ◽  
pp. 47-53 ◽  
Author(s):  
PING ZHANG
Keyword(s):  
Braid Group ◽  
Mapping Class Group ◽  
Class Group ◽  
Klein Bottle ◽  
Closed Surface ◽  
Group Extension ◽  
Braid Groups ◽  
Mapping Class ◽  
Group B ◽  
Central Automorphisms

It is shown that for the braid group Bn(M) on a closed surface M of nonnegative Euler characteristic, Out (Bn(M)) is isomorphic to a group extension of the group of central automorphisms of Bn(M) by the extended mapping class group of M, with an explicit and complete description of Aut (Bn(S2)), Aut (Bn(P2)), Out (Bn(S2)) and Out (Bn(P2)).

Central automorphisms of free nilpotent Lie algebras

2017 ◽  
Vol 16 (11) ◽  
pp. 1750205
Author(s):  
Özge Öztekin ◽  
Naime Ekici
Keyword(s):  
Lie Algebras ◽  
Finite Rank ◽  
Characteristic Zero ◽  
Sufficient Conditions ◽  
Nilpotency Class ◽  
Nilpotent Lie Algebra ◽  
Central Automorphism ◽  
Nilpotent Lie Algebras ◽  
Central Automorphisms

Let [Formula: see text] be the free nilpotent Lie algebra of finite rank [Formula: see text] [Formula: see text] and nilpotency class [Formula: see text] over a field of characteristic zero. We give a characterization of central automorphisms of [Formula: see text] and we find sufficient conditions for an automorphism of [Formula: see text] to be a central automorphism.

scholarly journals A FLAT LAGUERRE PLANE OF KLEINEWILLINGHÖFER TYPE V

2011 ◽  
Vol 91 (2) ◽  
pp. 257-274 ◽  
Author(s):  
JEROEN SCHILLEWAERT ◽  
GÜNTER F. STEINKE
Keyword(s):  
Parameter Family ◽  
Laguerre Plane ◽  
The Other ◽  
Flat Laguerre Plane ◽  
Laguerre Planes ◽  
Type V ◽  
Central Automorphisms ◽  
Kleinewillinghöfer Type

AbstractThe Kleinewillinghöfer types of Laguerre planes reflect the transitivity properties of certain groups of central automorphisms. Polster and Steinke have shown that some of the conceivable types for flat Laguerre planes cannot exist and given models for most of the other types. The existence of only a few types is still in doubt. One of these is type V.A.1, whose existence we prove here. In order to construct our model, we make systematic use of the restrictions imposed by the group. We conjecture that our example belongs to a one-parameter family of planes all of type V.A.1.

Groups with prescribed automorphism group: A clarification

1984 ◽  
Vol 27 (1) ◽  
pp. 59-60
Author(s):  
Derek J. S. Robinson
Keyword(s):  
Automorphism Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group A ◽  
Necessary And Sufficient ◽  
Central Automorphisms ◽  
Semisimple Subgroup

In Theorems 1 and 2 of [] necessary and sufficient conditions were given for a group G to have a finite automorphism group Aut G and a semisimple subgroup of central automorphisms AutcG. Recently it occurred to us, as a result of conversations with Ursula Webb, that these conditions could be stated in a much simpler and clearer form. Our purpose here is to record this reformulation. For an explanation ofterminology and notation we refer the reader to [1].

On central automorphisms that fix the centre elementwise

2007 ◽  
Vol 89 (4) ◽  
pp. 296-297 ◽  
Author(s):  
Mehdi Shabani Attar
Keyword(s):  
Central Automorphisms

scholarly journals On Central Automorphisms of Finitep-Groups

2013 ◽  
Vol 41 (3) ◽  
pp. 1117-1122 ◽  
Author(s):  
Mahak Sharma ◽  
Deepak Gumber
Keyword(s):  
Central Automorphisms

scholarly journals Some properties on $$\mathrm{IA_Z}$$-automorphisms of groups

2019 ◽  
Vol 9 (3) ◽  
pp. 691-695
Author(s):  
Hamid Taheri ◽  
Mohammd Reza R. Moghaddam ◽  
Mohammad Amin Rostamyari
Keyword(s):  
Present Article ◽  
Automorphisms Of Groups ◽  
Central Automorphisms

Abstract Let G be a group and $$\mathrm{IA}(G)$$ IA ( G ) denote the group of all automorphisms of G, which induce identity map on the abelianized group $$G_{ab}=G/G'$$ G ab = G / G ′ . Also the group of those $$\mathrm{IA}$$ IA -automorphisms which fix the centre element-wise is denoted by $$\mathrm{IA_Z}(G)$$ IA Z ( G ) . In the present article, among other results and under some condition we prove that the derived subgroups of finite p-groups, for which $$\mathrm{IA_Z}$$ IA Z -automorphisms are the same as central automorphisms, are either cyclic or elementary abelian.

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