caa a22 4500 445836830 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00209-010-0723-4 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0723-4 Chatterjee Pralay The Institute of Mathematical Sciences, C.I.T. Campus, 600113, Taramani, Chennai, India aut Automorphism invariant Cartan subgroups and power maps of disconnected groups [Elektronische Daten] [Pralay Chatterjee] We extend a well-known result of R. Steinberg on the existence of an invariant maximal torus under a semisimple automorphism of an algebraic group over an algebraically closed field. We show that the same result holds when the underlying field is of characteristic zero, but not necessarily algebraically closed. We next study surjectivity of the power maps $${g\mapsto g^{n}}$$ of disconnected algebraic groups of characteristic zero. In the case of disconnected real algebraic groups we apply our generalisation of Steinberg's result to obtain results on the surjectivity of the power maps. We also extend a result of A. Borel on weak exponentiality in real Lie groups by relating it with the surjectivity of the square map. Springer-Verlag, 2010 Cartan subgroups of algebraic groups nationallicence Power maps nationallicence Surjectivity nationallicence Weak-exponentiality nationallicence Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 221-233 0025-5874 269:1-2<221 2011 269 209 https://doi.org/10.1007/s00209-010-0723-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0723-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chatterjee Pralay The Institute of Mathematical Sciences, C.I.T. Campus, 600113, Taramani, Chennai, India aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 221-233 0025-5874 269:1-2<221 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer