Generating wreath products and their augmentation ideals

Andrea Lucchini

Rendiconti del Seminario Matematico della Università di Padova (1997)

  • Volume: 98, page 67-87
  • ISSN: 0041-8994

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Lucchini, Andrea. "Generating wreath products and their augmentation ideals." Rendiconti del Seminario Matematico della Università di Padova 98 (1997): 67-87. <http://eudml.org/doc/108450>.

@article{Lucchini1997,
author = {Lucchini, Andrea},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {generating sets; wreath products; finite permutation groups; finite soluble groups; symmetric groups; numbers of generators; augmentation ideals; group rings},
language = {eng},
pages = {67-87},
publisher = {Seminario Matematico of the University of Padua},
title = {Generating wreath products and their augmentation ideals},
url = {http://eudml.org/doc/108450},
volume = {98},
year = {1997},
}

TY - JOUR
AU - Lucchini, Andrea
TI - Generating wreath products and their augmentation ideals
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1997
PB - Seminario Matematico of the University of Padua
VL - 98
SP - 67
EP - 87
LA - eng
KW - generating sets; wreath products; finite permutation groups; finite soluble groups; symmetric groups; numbers of generators; augmentation ideals; group rings
UR - http://eudml.org/doc/108450
ER -

References

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  1. [1] J.H. Conway, - S.P. Norton - R.P. Parker - R.A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford (1985). Zbl0568.20001MR827219
  2. [2] M. Aschbacher - R. GURALNICK, Some applications of the first cohomology Group, J. Algebra, 90 (1984), pp. 446-460. Zbl0554.20017MR760022
  3. [3] K. Buzási - L.G. Kovács, The minimal number of generators of wreath products of nilpotent groups, Contemporary Mathematics, 93 (1989), pp. 115-121. Zbl0675.20023MR1003346
  4. [4] Yeo KokCHYE, Minimal generating sets for some wreath products of groups, Bull. Austral. Math. Soc., 9 (1973), pp. 127-136. Zbl0264.20030MR507007
  5. [5] J. Cossey - K. W. GRUENBERG - L. G. KOVÁCS, The presentation rank of a direct product of finite groups, J. Algebra, 28 (1974), pp. 597-603. Zbl0293.20033MR424969
  6. [6] F. DallaVOLTA - A. LUCCHINI, Generation of almost simple groups, J. Algebra, 178 (1995), pp. 194-223. Zbl0839.20021MR1358262
  7. [7] K.W. Gruenberg, Cohomological Topics in Group Theory, Lectures Notes Math. no. 143, Springer (1970). Zbl0205.32701MR279200
  8. [8] K.W. Gruenberg, Über die Relationen moduln einer endlichen Gruppe, Math. Z., 118 (1970). Zbl0213.30303MR276309
  9. [9] K.W. Gruenberg, Relation modules of finite groups, CBMS Monograph 25, Amer. Math. Soc., Providence (1976), pp. 408-421. Zbl0327.20019MR457538
  10. [10] K.W. Gruenberg, Groups of non zero presentation rank, Symposia Math., 17 (1976), pp. 215-224. Zbl0358.20045MR412298
  11. [11] P. Hall, The Eulerian functions of a group, Quart. J. Math., 7 (1936), pp. 134-151. Zbl0014.10402JFM62.0082.02
  12. [12] A. Lucchini, Some questions on the number of generators of a finite group, Rend. Sem. Mat. Univ. Padova, 83 (1990), pp. 201-222. Zbl0734.20012MR1066442
  13. [13] A. Lucchini, Generating wreath products, Arch. Math., 62 (1994), pp. 481-490. Zbl0811.20030MR1274101
  14. [14] A. Lucchini - F. Menegazzo, Generators for finite groups with a unique minimal normal subgroup, Rend. Sem. Mat. Univ. Padova, to appear. Zbl0895.20027MR1492976
  15. [15] S. Mac Lane, Homology, Springer (1963). Zbl0818.18001MR1344215
  16. [16] L. Ribes - K. Wong, On the minimal number of generators of certain groups, Groups St Andrews 1989, London Math. Soc. Lecture Note Series, 160, pp. 408-421. Zbl0742.20031MR1123995
  17. [17] K.W. Roggenkamp, Relation modules of finite groups and related topics, Algebra i Logika, 12 (1973), pp. 351-369. Zbl0286.20045MR387391
  18. [18] K.W. Roggenkamp, Integral representation and presentations of finite groups, Lectures Notes Math. no. 744, Springer (1979). Zbl0431.20001
  19. [19] U. Stammbach, Cohomological characterizations of finite solvable and nilpotent groups, J. Pure Appl. Algebra, 11 (1977), pp. 293-301. Zbl0374.20060MR466345
  20. [20] K.W. Gruenberg - K.W. Roggenkamp, Decomposition of the relation modules of a finite group, J. London Math. Soc., 12 (1976), pp. 262-266. Zbl0325.20015MR390030

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