On the lattice automorphisms of certain simple algebraic groups

Mauro Costantini

Rendiconti del Seminario Matematico della Università di Padova (1993)

  • Volume: 90, page 141-157
  • ISSN: 0041-8994

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Costantini, Mauro. "On the lattice automorphisms of certain simple algebraic groups." Rendiconti del Seminario Matematico della Università di Padova 90 (1993): 141-157. <http://eudml.org/doc/108299>.

@article{Costantini1993,
author = {Costantini, Mauro},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {index-preserving; induced by automorphism; simple algebraic groups; autoprojectivity; strongly lattice determined},
language = {eng},
pages = {141-157},
publisher = {Seminario Matematico of the University of Padua},
title = {On the lattice automorphisms of certain simple algebraic groups},
url = {http://eudml.org/doc/108299},
volume = {90},
year = {1993},
}

TY - JOUR
AU - Costantini, Mauro
TI - On the lattice automorphisms of certain simple algebraic groups
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1993
PB - Seminario Matematico of the University of Padua
VL - 90
SP - 141
EP - 157
LA - eng
KW - index-preserving; induced by automorphism; simple algebraic groups; autoprojectivity; strongly lattice determined
UR - http://eudml.org/doc/108299
ER -

References

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  1. [1] M. Aschbacher - G.M. Seitz, Involutions in Chevalley groups over fields of even order, Nagoya Math. J., 63 (1976), pp. 1-91. Zbl0359.20014MR422401
  2. [2] M. Aschbacher - G.M. Seitz, Correction to «Involutions in Chevalley groups over fields of even order», Nagoya Math. J., 72 (1978), pp. 135-136. Zbl0391.20010MR514895
  3. [3] P. Bala - R.W. Carter, Classes of unipotent elements in simple algebraic groups. I, Math. Proc. Cambridge Philos. Soc., 79 (1976), pp. 401-425. Zbl0364.22006MR417306
  4. [4] P. Bala - R.W. Carter, Classes of unipotent elements in simple algebraic groups. II, Math. Proc. Cambridge Philos. Soc., 80 (1976), pp. 1-18. Zbl0364.22007MR417307
  5. [5] R.W. Carter, Finite Groups of Lie Type, John Wiley, London (1985). Zbl0567.20023MR794307
  6. [6] C. Cooper, Power automorphisms of a group, Math. Zeit., 107 (1968), pp. 335-356. Zbl0169.33801MR236253
  7. [7] M. Costantini, Sul gruppo delle autoproiettività di PSL(3, q), Riv. Mat. Pura Appl. Univ. Udine, 4 (1989), pp. 79-88. Zbl0712.20013
  8. [8] M. Costantini, Autoprojectivities and automorphisms of certain algebraic groups, Rend. Accad. Naz. Sci. XL, Mem. Mat., 110 (1992), Vol. XVI, fasc. 7, pp. 99-114. Zbl0830.20050MR1205747
  9. [9] J. Dieudonné, Le géométrie des groupes classiques, Ergebnisse der Mathematik und ihrer Grenzgebiete, 5 (1955), Springer. Zbl0067.26104MR72144
  10. [10] C.S. Holmes, Projectivities of free products, Rend. Sem. Mat. Univ. Padova, 42 (1969), pp. 341-387. Zbl0245.20031MR268286
  11. [11] C. Metelli, Sugli isomorfismi reticolari di PSL2 (pf), Rend. Acc. Naz. Lincei Cl. Scienze, s. VIII, vol. XLVII, fasc. 6 (1969). Zbl0218.20043
  12. [12] C. Metelli, I gruppi semplici minimali sono individuati reticolarmente in senso stretto, Rend. Sem. Mat. Univ. Padova, 45 (1971), pp. 367-378. Zbl0248.20014MR310076
  13. [13] K. Pommerening, Über die unipotenten Klassen reduktiver Gruppen, J. Algebra, 49 (1977), pp. 525-536. Zbl0367.20046MR480767
  14. [14] K. Pommerening, Über die unipotenten Klassen reduktiver Gruppen II, J. Algebra, 65 (1980), pp. 373-398. Zbl0437.20034MR585729
  15. [15] E.L. Sadovski, Über die Structurisomorphismen von Freigruppen, Doklady, 23 (1941), pp. 171-174. 
  16. [16] E.L. Sadovski, Projectivities and isomorphisms of nilpotent groups, Izv. Akad. Nauk SSSR, Ser. Mat, 29 (1) (1965), pp. 171-208. MR171848
  17. [17] R. Schmidt, Verbandsautomorphismen der alternierenden Gruppen, Math. Zeit., 154 (1977), pp. 71-78. Zbl0334.20009MR447419
  18. [18] L. Shangzhi, On the subgroup lattice characterization of finite simple groups of Lie type, Chin. Ann. B, 4 (2) (1983), pp. 165-169. Zbl0527.20015MR714781
  19. [19] T.A. Springer, Linear Algebraic Groups, Birkhäuser, Boston (1981). Zbl0453.14022MR632835
  20. [20] R. Steinberg, Lectures on Chevalley groups, Yale University (1967). MR466335
  21. [21] M. Suzuki, Structure of a Group and the Structure of its Lattice of Subgroups, Springer, Berlin-Göttingen-Heidelberg (1956). Zbl0070.25406MR83487
  22. [22] H. Völklein, On the lattice automorphisms of the finite Chevalley groups, Indag. Math, 89 (1986), pp. 213-228. Zbl0628.20022MR849720
  23. [23] H. Völklein, On the lattice automorphisms of SLn (q) and PSLn (q), Rend. Sem. Mat. Univ. Padova, 76 (1986), pp. 207-217. Zbl0632.20015MR881571
  24. [24] G. Zacher, Sul reticolo dei sottogruppi di un gruppo di permutazioni, Padova, Cedam (1965). 
  25. [25] G. Zacher, Sul reticolo dei sottogruppi del gruppo simmetrico, Rend. Ist. di Matem. Univ. di Trieste, Vol. IX, fasc. 1-2 (1977), pp. 122.126. 
  26. [26] G. Zacher, Una caratterizzazione reticolare della finitezza dell'indice di un sottogruppo di un gruppo, Rend. Acc. Naz. Lincei Cl. Scienze, s. VIII, vol. LXIX, fasc. 6 (1980). 

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