If A is a nontrivial torsion-free, locally cyclic group with no nontrivial divisible quotients, and G is the split extension of A by a group of order 2 acting on A by means of the inverting map, then G is isomorphic to Aut G. We prove that in no other case the full automorphism group of a group is infinite and locally dihedral.
Infinite locally dihedral groups as automorphism groups / Celentani, MARIA ROSARIA; Leone, Antonella; Nicotera, Chiara. - In: RICERCHE DI MATEMATICA. - ISSN 1827-3491. - 63 (suppl 1):(2014), pp. 69-73. [10.1007/s11587-014-0201-0]
Infinite locally dihedral groups as automorphism groups
CELENTANI, MARIA ROSARIA;LEONE, ANTONELLA;NICOTERA, Chiara
2014
Abstract
If A is a nontrivial torsion-free, locally cyclic group with no nontrivial divisible quotients, and G is the split extension of A by a group of order 2 acting on A by means of the inverting map, then G is isomorphic to Aut G. We prove that in no other case the full automorphism group of a group is infinite and locally dihedral.File in questo prodotto:
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