next up previous
Next: About this document Up: A Review of ``Subgroup Previous: A Review of ``Subgroup

References

1
R. W. Baddeley and A. Lucchini, On representing finite lattices as intervals in subgroup lattices of finite groups, preprint.

2
R. Baer, The significance of the system of subgroups for the structure of the group, Amer. J. Math. 61 (1939), 1-44.

3
R. Baer, A unified theory of projective spaces and finite Abelian groups, Trans. Amer. Math. Soc. 52 (1942), 283-343.

4
G. Boole, An Investigation into the Laws of Thought, 1854, Reprinted by Open Court Publishing Co., Chicago, 1940.

5
R. G. Burns and S. Oates-Williams, Varieties of groups and normal-subgroup lattices--a survey, Algebra Universalis 32 (1994), 145-152.

6
R. Dedekind, Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen Teiler, Festschrift der Herzogl. technische Hochschule zur Naturforscher-Versammlung, Braunschweig (1897), Reprinted in ``Gesammelte mathematische Werke'', Vol. 2, pp. 103-148, Chelsea, New York, 1968.

7
R. Dedekind, Über die von drei Moduln erzeugte Dualgruppe, Math. Annalen 53 (1900), 371-403.

8
R. Freese, Finitely based modular congruence varieties are distributive, Algebra Universalis 32 (1994), 104-114.

9
R. Freese and B. Jónsson, Congruence modularity implies the Arguesian identity, Algebra Universalis 6 (1976), 225-228.

10
M. Hall, the Theory of Groups, Chelsea, New York, 1959.

11
A. Yu. Ol'shanskiĭ, An infinite group with subgroups of prime orders, Inv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 309-321 (Russian).

12
A. Yu. Ol'shanskiĭ, Groups of bounded period with subgroups of prime order, Algebra i Logic 21 (1982), 553-618 (Russian).

13
I. Kaplansky, Infinite Abelian Groups, University of Michigan Press, Ann Arbor, 1969, Revised edition.

14
P. Köhler, M7 as an interval in a subgroup lattice, Algebra Universalis 17 (1983), 263-266.

15
L. Lady, Finite Rank Torsion Free Modules over Dedekind Domains, preliminary version available at http://www.math.hawaii.edu/ tex2html_wrap_inline496 lee.

16
A. Lucchini, Intervals in subgroup lattices of finite groups, Communications in Algebra 22 (1994), 529-549.

17
A. Lucchini, Representations of certain lattices as intervals in subgroup lattices, J. Algebra 164 (1994), 85-90.

18
Ralph McKenzie, George McNulty, and Walter Taylor, Algebras, Lattices, Varieties, Volume I, Wadsworth and BrooksCole, Monterey, California, 1987.

19
O. Ore, On the foundations of abstract algebra, I, Ann. Math. 36 (1935), 406-437.

20
O. Ore, On the foundations of abstract algebra, II, Ann. Math. 37 (1936), 265-292.

21
O. Ore, Structures and group theory, I, Duke Math. J. 3 (1937), 149-173.

22
O. Ore, Structures and group theory, II, Duke Math. J. 4 (1938), 247-269.

23
P. P. Pálfy, On Feit's examples of intervals in subgroup lattices, J. Algebra 116 (1988), 471-479.

24
P. P. Pálfy and P. Pudlák, Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups, Algebra Universalis 11 (1980), 22-27.

25
P. P. Pálfy and C. Szabó, Congruence varieties of groups and Abelian groups, Lattice Theory and its Applications (K. A. Baker and R. Wille, eds.), Heldermann Verlag, Lemgo, Germany, 1995, In Celebration of Garrett Birkhoff's 80th Birthday, Research and Exposition in Mathematics, Vol. 23, Darmstadt, Germany, June 13-17, 1991, pp. 163-184.

26
P. P. Pálfy and C. Szabó, An identity for subgroup lattices of Abelian groups, Algebra Universalis 33 (1995), 191-195.

27
E. Schröder, Algebra der Logik, Leipzig, 1890-1995, 3 volumes.

28
M. Suzuki, Structure of a Group and the Structure of its Lattice of Subgroups, Springer Verlag, Berlin, 1956.

29
J. T'uma, Intervals in subgroup lattices of infinite groups, J. Algebra 125 (1989), 367-399.



Ralph Freese
Wed Feb 28 13:55:46 HST 1996