Complements of Connected Subgroups in Algebraic Groups

Peter Plaumann; Karl Strambach; Giovanni Zacher

Rendiconti del Seminario Matematico della Università di Padova (2006)

  • Volume: 115, page 253-264
  • ISSN: 0041-8994

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Plaumann, Peter, Strambach, Karl, and Zacher, Giovanni. "Complements of Connected Subgroups in Algebraic Groups." Rendiconti del Seminario Matematico della Università di Padova 115 (2006): 253-264. <http://eudml.org/doc/108680>.

@article{Plaumann2006,
author = {Plaumann, Peter, Strambach, Karl, Zacher, Giovanni},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {connected groups; subgroup lattices; connected closed subgroups; relatively complemented lattices of connected subgroups; Frattini subgroups; intervals},
language = {eng},
pages = {253-264},
publisher = {Seminario Matematico of the University of Padua},
title = {Complements of Connected Subgroups in Algebraic Groups},
url = {http://eudml.org/doc/108680},
volume = {115},
year = {2006},
}

TY - JOUR
AU - Plaumann, Peter
AU - Strambach, Karl
AU - Zacher, Giovanni
TI - Complements of Connected Subgroups in Algebraic Groups
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2006
PB - Seminario Matematico of the University of Padua
VL - 115
SP - 253
EP - 264
LA - eng
KW - connected groups; subgroup lattices; connected closed subgroups; relatively complemented lattices of connected subgroups; Frattini subgroups; intervals
UR - http://eudml.org/doc/108680
ER -

References

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  2. [2] A. BOREL, Linear Algebraic Groups, Springer-Verlag 1991. Zbl0726.20030MR1102012
  3. [3] M. CONSTANTINI - G. ZACHER, The finite simple groups have complemented subgroup lattices, Pac. J. Math., 213 (2004), pp. 245-251. Zbl1062.20025MR2036918
  4. [4] L. DI MARTINO - M.C. TAMBURINI BELLANI, On the solvability of finite IMgroups, Ist. Lombardo Rend., 115 (1981), pp. 235-242. Zbl0568.20030MR780472
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  6. [6] W. GASCHÜTZ, Über die F-Untergruppe endlicher Gruppen, Math. Zeitschrift 58 (1953), pp. 160-170. Zbl0050.02202MR57873
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  11. [11] P. PLAUMANN - K. STRAMBACH - G. ZACHER, Der Verband der zusammenhängenden Untergruppen einer kommutativen algebraischen Gruppe, Arch. Math., 85 (2005), pp. 37-48. Zbl1114.20026MR2155108
  12. [12] M. ROSENLICHT, Some basic theorems on algebraic groups, Amer. J. Math., 78 (1956), pp. 401-443. Zbl0073.37601MR82183
  13. [13] M. ROSENLICHT, Extensions of vector groups by Abelian vareties, Amer. J. Math., 80 (1958), pp. 685-714. Zbl0091.33303MR99340
  14. [14] R. SCHMIDT, Subgroup Lattices of Groups, De Gruyter expositions in mathematics 14, de Gruyter 1994. Zbl0843.20003MR1292462
  15. [15] G. ZACHER, Caratterizzazione dei gruppi risolubili d'ordine finite complementati, Rend. Sem. Mat. Univ. Padova, 22 (1953), pp. 113-122. Zbl0051.25802MR57878
  16. [16] G. ZACHER, Determinazione dei gruppi finiti relativamente complementati, Rend. Acc. Sci. Fis. Mat. Napoli, 19 (1952), pp. 200-206. Zbl0053.20901MR61106
  17. [17] G. ZACHER, Costruzione dei gruppi finiti a sottogruppi di Frattini identico, Rend. Sem. Mat. Univ. Padova, 21 (1952), pp. 383-394. Zbl0048.01501MR53103

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