Pseudocomplementation in (Normal) Subgroup Lattices

REFERENCES

• Aschbacher , M. ( 2000 ). Finite Group Theory. , 2nd ed. Cambridge Studies in Advanced Mathematics 10. Cambridge : Cambridge University Press .
   Google Scholar
• Baer , R. ( 1939 ). The significance of the system of subgroups for the structure of the group . Amer. J. Math. 61 : 1 – 44 .
   Google Scholar
• Birkhoff , G. ( 1967 ). Lattice Theory . Providence , RI : Amer. Math. Soc .
   Google Scholar
• Brandl , R. , Cutolo , G. , Rinauro , S. ( 1995 ). Posets of subgroups of groups and distributivity. Boll. U.M.I. 9-A:217–223 .
   Google Scholar
• Călugăreanu , Gr. G. ( 1986 ). Abelian groups with pseudocomplemented lattice of subgroups . Studia Univ. Babeş-Bolyai Cluj-Napoca 31 : 39 – 41 .
   Google Scholar
• Glivenko , V. ( 1929 ). Sur quelques points de la logique de M. Brouwer . Bull. Acad. Sc. Belgique 15 : 183 – 188 .
   Google Scholar
• Grätzer , G. ( 1978 ). General Lattice Theory . New York : Academic Press .
   Google Scholar
• Huppert , B. ( 1967 ). Endliche Gruppen I . Die Grundlehren der Mathematischen Wissenschaften, Band 134 . Berlin , New York : Springer-Verlag .
   Google Scholar
• Ore , O. ( 1938 ). Structures and group theory II . Duke Math. J. 4 : 247 – 269 .
   Google Scholar
• Pazderski , G. ( 1987 ). On groups for which the lattice of normal subgroups is distributive . Beiträge zur Algebra und Geometrie 24 : 185 – 200 .
   Google Scholar
• Rottlaender , A. ( 1928 ). Nachweis der Existenz nicht-isomorpher Gruppen von gleicher Situation der Untergruppen . Math. Z. 28 : 641 – 653 .
   Google Scholar
• Schmidt , R. ( 1994 ). Subgroup Lattices of Groups . de Gruyter Expositions in Mathematics 14. Berlin : de Gruyter .
   Google Scholar
• Schmidt , R. ( 2000 ). New results and methods in the theory of subgroup lattices of groups . In: Curzio , M. , De Giovanni , F. , eds. Quaderni di Mat . Vol. 8 . ( Topics in Infinite Groups) , Rome : Aracne , pp. 239 – 275 .
   Google Scholar
• Suzuki , M. ( 1951 ). On the lattice of subgroups of finite groups . Trans. Amer. Math. Soc. 70 : 345 – 371 .
   Web of Science ®Google Scholar
• Suzuki , M. ( 1951 ). On the L-homomorphisms of finite groups . Trans. Amer. Math. Soc. 70 : 372 – 386 .
   Google Scholar
• Suzuki , M. (1955). On finite groups with cyclic Sylow subgroups for all odd primes. Amer. J. Math. 77:657–691.
   Google Scholar
• Suzuki , M. ( 1956 ). Structure of a Group and the Structure of its Lattice of Subgroups . Ergebnisse der Mathematik und ihrer Grenzgebiete , Neue Folge , Heft 10. Berlin-Göttingen-Heidelberg : Springer-Verlag .
   Google Scholar
• Suzuki , M. ( 1982/1986 ). Group Theory, I, II. Berlin : Springer-Verlag .
   Google Scholar
• Tărnăuceanu , M. ( 2004 ). On groups whose lattices of subgroups are pseudocomplemented . Fuzzy Systems & Artificial Intelligence 10 : 45 – 49 .
   Google Scholar
• Tărnăuceanu , M. ( 2005 ). Pseudocomplemented groups . An. Univ. “Al. I. Cuza”, Iaşi, Math. (1) 51 : 201 – 205 .
   Google Scholar
• Tărnăuceanu , M. ( 2006 ). Complementation in subgroup lattices . Sci. Ann. Univ. Agric. Sci. Vet. Med. 49 : 285 – 303 .
   Google Scholar
• Tărnăuceanu , M. ( 2006 ). Complementation in normal subgroup lattices . Sci. Ann. Univ. Agric. Sci. Vet. Med. 49 : 305 – 322 .
   Google Scholar
• Tărnăuceanu , M. ( 2006 ). Groups Determined by Posets of Subgroups. Bucureşti, Ed. Matrix Rom .
   Google Scholar
• Toh , K. H. ( 1973 ). Groups with normal subgroups possessing subnormal complements . Proc. Amer. Math. Soc. (2) 41 : 378 – 380 .
   Google Scholar
• Whitson , G. ( 1978 ). Finite groups whose subgroup, composition subgroup, or normal subgroup lattice is an ortholattice . Algebra Universalis 8 : 123 – 127 .
   Google Scholar
• Wiegold , J. ( 1960 ). On direct factors in groups . J. London Math. Soc. 35 : 310 – 320 .
   Google Scholar
• Communicated by M. Kambites.
   Google Scholar