ON AUTOMORPHISMS OF FINITE GROUPS Export

@article{citeulike:6070165, abstract = {We consider orbits of elements of a finite group G with respect to the action on G of a cyclic automorphism group generated by ph. We obtain sufficient conditions for the existence of an orbit whose length is equal to the order of the automorphism ph. Namely, such an orbit exists for any automorphism ph of a semisimple or nilpotent finite group G and for an automorphism ph of an arbitrary finite group G when the orders of ph and G are relatively prime. In the general case, the question of the existence of such an orbit for an automorphism of a finite group is answered negatively; a series of counterexamples is constructed. Nevertheless, the order of an automorphism ph of a finite group G is in all cases bounded by the order of G. Bibliography: 1 item.}, author = {Horosevskii, M. V.}, citeulike-article-id = {6070165}, citeulike-linkout-0 = {http://dx.doi.org/10.1070/SM1974v022n04ABEH001707}, doi = {10.1070/SM1974v022n04ABEH001707}, journal = {Mathematics of the USSR-Sbornik}, keywords = {automorphisms, group-theory, representation-theory}, number = {4}, pages = {584--594}, posted-at = {2009-11-04 16:35:13}, priority = {2}, title = {ON AUTOMORPHISMS OF FINITE GROUPS}, url = {http://dx.doi.org/10.1070/SM1974v022n04ABEH001707}, volume = {22}, year = {1974} }

TY - JOUR ID - citeulike:6070165 L3 - citeulike-article-id:6070165 N2 - We consider orbits of elements of a finite group G with respect to the action on G of a cyclic automorphism group generated by ph. We obtain sufficient conditions for the existence of an orbit whose length is equal to the order of the automorphism ph. Namely, such an orbit exists for any automorphism ph of a semisimple or nilpotent finite group G and for an automorphism ph of an arbitrary finite group G when the orders of ph and G are relatively prime. In the general case, the question of the existence of such an orbit for an automorphism of a finite group is answered negatively; a series of counterexamples is constructed. Nevertheless, the order of an automorphism ph of a finite group G is in all cases bounded by the order of G. Bibliography: 1 item. IS - 4 JF - Mathematics of the USSR-Sbornik EP - 594 TI - ON AUTOMORPHISMS OF FINITE GROUPS VL - 22 SP - 584 KW - automorphisms KW - group-theory KW - representation-theory AU - Horosevskii, MV PY - 1974/// UR - http://dx.doi.org/10.1070/SM1974v022n04ABEH001707 ER -