Notes, articles, books ...

Articles

 Simplicial complexes & posets
  1. Baddeley, R., Lucchini, A., On Representing Finite Lattices as Intervals in Subgroup Lattices of Finite Groups, J. of Algebra 196 (1997), 1--100.
  2. Brandl, R., Verardi, L., Finite groups with few conjugacy classes of subgroups, Rend. Sem. Mat. Univ. Padova, 87 (1992), 267--280.
  3. Brown, K.S., The Coset Poset and Probabilistic Zeta Function of a Finite Group, Journal of Algebra 225, (2000), 989--1012.
  4. Bryce, R.A., Hawkes, T.O., Lattices in the Frame of a Finite Soluble Group, to appear.
  5. Costantini, M., Zacher, G., The finite simple groups have complemented subgroup lattice, Pacific J. of Math. 213, No. 2, (2004), 245--250.
  6. Fumagalli, F., Simplicial  Complexes in Finite Groups, PhD Thesis.
  7.  Kratzer, C., Thévenaz, J., Fonction de Möbius d'un groupe fini et anneau de Burnside, Comm. Math. Helv. 59 (1984), no.3, 425--438.
  8.  Lucido, M.S., On the poset of non-trivial proper subgroups of a finite group, J. Algebra Appl. 2, No. 2, (2003), 165--168.
  9.  Lucido, M.S., Prime graph components of finite almost simple groups, Rend. Sem. Mat. Univ. Padova, 102, (1999), 1--22. (Addendum)
  10. Pakianathan, J., Yalcin, E., On Commuting and Noncommuting Complexes, J. of Algebra 236, (2001), 396--418.
  11. Ramras, D.A., Connectivity of the coset poset and the subgroup poset of a group,  J. Group Theory 8, (2005), 719--746.
  12. Shareshian, J., Combinatorial properties of subgroup lattices of finite groups, PhD Thesis.
  13. Shareshian, J., On the shellability of the order complex of the subgroup lattice of a finite group, Trans. Amer. Math. Soc. 353, No. 7, (2001) 2689--2703.
  14. Shareshian, J., Topology of order complexes of intervals in subgroup lattices, J. of Algebra 268, (2003) 677--686.
  15. Shareshian, J., Topology of subgroup lattices of symmetric and alternating groups, J. of Comb. Theory, Series A, 104, (2003) 137--155.
  16. Shareshian, J., Hypergraph matching complexes and Quillen complexes of symmetric groups, J. of Comb. Theory, Series A, 106, (2004) 299--314.
  17. Welker, V., Equivariant Homotopy of Posets and Some Applications to Subgroup Lattice, J. of Comb. Theory, Series A 69, (1995), 61--86.
  18. Woodroofe, R., Shelling the coset poset, J. of Comb. Theory, Series A 114 (2007), 733--746.
Burnside ring
  1. Dress, A., A characterisation of solvable groups, Math. Z. 110 (1969) 213--217.

Graph Theory
  1. K. Kutnar, D. Marusic, Hamilton cycles and paths in vertex-transitive graphs - Current directions, Discrete Math. 309 (2009), 5491--5500.
  2. Cai Heng Li, On Cayley Isomorphisms of Finite Cayley Graphs - a Survey
Expander Graphs
  1. M. Kassabov, A. Lubotzky and N. Nikolov , Finite Simple Groups as Expanders, Proc. Natl. Acad. Sci. USA, 103 (2006), no. 16, 6116--6119
  2. R. Meshulam, A. Wigderson, Expanders in Group Algebras,  Combinatorica, 24 (2004), no. 4, 659--680.
  3. M. Kassabov, Symmetric Groups and Expanders Graphs,  Invent. Math. 170 (2007), no. 2, 327--354.
  4. O. Reingold, S. Vadhan and A. Wigderson, Entropy Waves, the Zig-Zag Graph Product and New Constant-degree Expanders,
  5. E. Rozenman, A. Shalev, A. Wigderson, Iterative Construction of Cayley Expander Graphs
  6. N. Alon, A. Lubotzky, A. Wigderson, Semidirect Product in Groups and Zig-Zag Product in Graphs: Connections and Applications, 
  7. S. Hoory, N. Linial and A. Wigderson, Expander Graphs and their Applications, Bulletin (New Series) of the AMS, 43 (2006), 439--561.


Automorphisms

Free groups & Presentations
  1. Ward, M.,  Bases for  polynilpotent groups, Proc. London Math. Soc. (3), 24 (1972), 409--431.
Coverings of finite groups
  1. Bryce, R.A., Serena, L., Some remarks on groups with nilpotent minimal covers, to appear.
  2. Tomkinson, M.J., Groups as the union of proper subgroups, Math. Scand. 81 (1997), 191--198.
  3. Zappa, G., Partitions and other coverings of finite groups, Illinois J. of Math., 47, No. 1 (2003), 571--580.
Nonabelian Tensor Squares
  1. Blyth, R.D., Morse R.F., Computing the nonabelian tensor squares of polycyclic groups, to appear.
  2. Blyth, R.D., Moravec, P., Morse, R.F., On the nonabelian tensor squares of free nilpotent groups of finite rank, to appear.
  3. Brown R., Johnson, D.L. Robertson, E.F., Some computations of nonabelian tensor products of groups, J. Algebra, 111 (1987), no. 1, 177--202.
  4. Kappe L.C., Visscher M.P., Sarmin N.H., Two-generator two-groups of class two and their nonabelian tensor squares, Glasgow Math. J., 41 (1999), 417--430.
  5. Magidin, A., On the capability of finite groups of class two and prime exponent, to appear.
  6. McDermott, A., The nonabelian tensor product of groups, PhD Thesis.
  7. Morse, R.F., Advances in Computing the Nonabelian Tensor Square of Polycyclic Groups, Irish Math. Soc. Bulletin 56 (2005), 115--123.
  8. Rocco N.R., On a Construction Related to the Non-Abelian Tensor Square of a Group, Bol. Soc. Bras. Mat., 22, No. 1, (1991), 63--79.
  9. Rocco N.R., A Presentation for a Crossed Embedding of Finite Solvable Groups, Comm. in Algebra, 22(6), (1994), 1975--1998.
  10. Whitehead, J.H.C., A certain exact sequence, Ann. of Math (2) 52, (1950), 51--110.

Products of subgroups


Maximal subgroups in finite groups
  1. Aschbacher, M., On the maximal subgroups of the finite classical groups, Invent. Math. 76 (1984), 469--514.
  2. Cannon, J.J., Holt, D.F., Computing maximal subgroups of finite groups, to appear.
  3. Liebeck, M.W., Seitz, G.M., A survey of maximal subgroups of exceptional groups of Lie type,  Groups combinatorics & geometry (Durham,2001), 139--146.
Classification
  1. Aschbacher, M., The Status of the Classification of the Finite Simple Groups, Notices of the AMS, 51, No. 7 (2004), 736--740.
  2. Solomon, R., A Brief History of the Classification of the Finite Simple Groups, Bull. Amer. Math. Soc., 38, No. 3, (2001), 315--352.
  3. ???, The Monster, ???

Notes
  1. Cameron, P.J., Notes on classical groups, London 2000.
  2. Cameron, P.J., Notes on counting, London 2003.
  3. Casolo C., Simplicial Complexes in Finite Groups, Cortona 2001.
  4. Milne, J.S., Algebraic Groups and Arithmetic Groups, 2006.
  5. Navarro, Characters, Fields and Degrees, Milano 2007 (Note di P. Spiga).
  6. Fernandez-Alcober G.A., An introduction to finite p-groups: regular p-groups and groups of maximal class.

Books
  1. R. Steinberg, Lectures on Chevalley Groups, 1966 (1, 2, 3, 4, 5, 6)
  2. Kurzweil H., Stellmacher B. The theory of finite groups: an introduction, Springer, 2004.
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