Totally Variant Sets in Finite Groups and Vector Spaces
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 701-710
Voir la notice de l'article provenant de la source Cambridge University Press
We are concerned here with the question of which finite groups and vector spaces possess subsets which are moved by every non-identity automorphism (in the vector-space case—non-singular linear transformation). We find that this is the case for all but four finite-dimensional vector spaces (2-, 3-, and 4-dimensional space over Z 2, 2-dimensional space over Z 3), and for all finite groups except for those corresponding to the vector-space exceptions, and the quaternion group of order eight. The question was first posed to the authors, in the vector-space case, by Morris Marx.
Hoffman, Frederick; Welch, Lloyd R. Totally Variant Sets in Finite Groups and Vector Spaces. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 701-710. doi: 10.4153/CJM-1968-068-5
@article{10_4153_CJM_1968_068_5,
author = {Hoffman, Frederick and Welch, Lloyd R.},
title = {Totally {Variant} {Sets} in {Finite} {Groups} and {Vector} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {701--710},
year = {1968},
volume = {20},
number = {1},
doi = {10.4153/CJM-1968-068-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-068-5/}
}
TY - JOUR AU - Hoffman, Frederick AU - Welch, Lloyd R. TI - Totally Variant Sets in Finite Groups and Vector Spaces JO - Canadian journal of mathematics PY - 1968 SP - 701 EP - 710 VL - 20 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-068-5/ DO - 10.4153/CJM-1968-068-5 ID - 10_4153_CJM_1968_068_5 ER -
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