Results 181 to 190 of about 32,457 (190)
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CENTRAL AUTOMORPHISMS THAT ARE ALMOST INNER
Communications in Algebra, 2001An automorphism σ of a group G is central if σ commutes with every automorphism in Inn(G), the group of inner automorphisms of G, or equivalently, if g −1 σ(g) lies in the centre Z(G) of G, for all...
D. J. McCaughan, M. J. Curran
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ON INNER AUTOMORPHISMS AND CENTRAL AUTOMORPHISMS OF NILPOTENT GROUP OF CLASS 2
Journal of Algebra and Its Applications, 2011Let G be a group and let Aut c(G) be the group of all central automorphisms of G. Let C* = C Aut c(G)(Z(G)) be the set of all central automorphisms of G fixing Z(G) elementwise. In this paper, we prove that if G is a finitely generated nilpotent group of class 2, then C* ≃ Inn (G) if and only if Z(G) is cyclic or Z(G) ≃ Cm × ℤr where [Formula: see ...
Mehri Akhavan-Malayeri, Zahedeh Azhdari
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Central Automorphisms and Inner Automorphisms in Finitely Generated Groups
Communications in Algebra, 2016Let G be a group and Autc(G) be the group of all central automorphisms of G. We know that in a finite p-group G, Autc(G) = Inn(G) if and only if Z(G) = G′ and Z(G) is cyclic. But we shown that we cannot extend this result for infinite groups. In fact, there exist finitely generated nilpotent groups of class 2 in which G′ =Z(G) is infinite cyclic and ...
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Automorphisms and Finite Inner Maps
1998The group Aut G and the semigroup Hol G, which were already studied in 8.4, are central to Sections 1 and 2. For bounded domains G, every sequence fn ∈ Hol G has a convergent subsequence (Montel); this fact has surprising consequences. For example, in H.
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Loops Whose Inner Mappings are Automorphisms
The Annals of Mathematics, 1956R. H. Bruck, Lowell J. Paige
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