Periodic linear groups factorized by mutually permutable subgroups

Maria Ferrara; Marco Trombetti

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 4, page 1229-1254
  • ISSN: 0011-4642

Abstract

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The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic linear groups (showing that the commutator subgroups and the intersection of mutually permutable subgroups are subnormal subgroups of the whole group), and, in this paper, we completely generalize all other main results of J. C. Beidleman, H. Heineken (2005) to (homomorphic images of) periodic linear groups.

How to cite

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Ferrara, Maria, and Trombetti, Marco. "Periodic linear groups factorized by mutually permutable subgroups." Czechoslovak Mathematical Journal 73.4 (2023): 1229-1254. <http://eudml.org/doc/299452>.

@article{Ferrara2023,
abstract = {The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic linear groups (showing that the commutator subgroups and the intersection of mutually permutable subgroups are subnormal subgroups of the whole group), and, in this paper, we completely generalize all other main results of J. C. Beidleman, H. Heineken (2005) to (homomorphic images of) periodic linear groups.},
author = {Ferrara, Maria, Trombetti, Marco},
journal = {Czechoslovak Mathematical Journal},
keywords = {mutually permutable subgroup; periodic linear group},
language = {eng},
number = {4},
pages = {1229-1254},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic linear groups factorized by mutually permutable subgroups},
url = {http://eudml.org/doc/299452},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Ferrara, Maria
AU - Trombetti, Marco
TI - Periodic linear groups factorized by mutually permutable subgroups
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1229
EP - 1254
AB - The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic linear groups (showing that the commutator subgroups and the intersection of mutually permutable subgroups are subnormal subgroups of the whole group), and, in this paper, we completely generalize all other main results of J. C. Beidleman, H. Heineken (2005) to (homomorphic images of) periodic linear groups.
LA - eng
KW - mutually permutable subgroup; periodic linear group
UR - http://eudml.org/doc/299452
ER -

References

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  1. Alejandre, M. J., Ballester-Bolinches, A., Cossey, J., 10.1016/j.jalgebra.2003.01.002, J. Algebra 276 (2004), 453-461. (2004) Zbl1083.20019MR2058452DOI10.1016/j.jalgebra.2003.01.002
  2. Amberg, B., Franciosi, S., Giovanni, F. de, Products of Groups, Oxford Mathematical Monographs. Clarendon Press, Oxford (1992). (1992) Zbl0774.20001MR1211633
  3. Asaad, M., Shaalan, A., 10.1007/BF01195210, Arch. Math. 53 (1989), 318-326. (1989) Zbl0685.20018MR1015994DOI10.1007/BF01195210
  4. Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M., 10.1515/9783110220612, de Gruyter Expositions in Mathematics 53. Walter de Gruyter, Berlin (2010). (2010) Zbl1206.20019MR2762634DOI10.1515/9783110220612
  5. Beidleman, J., Heineken, H., 10.1515/jgth.1999.027, J. Group Theory 2 (1999), 377-392. (1999) Zbl0941.20026MR1718750DOI10.1515/jgth.1999.027
  6. Beidleman, J. C., Heineken, H., 10.1007/s00013-005-1200-2, Arch. Math. 85 (2005), 18-30. (2005) Zbl1103.20015MR2155106DOI10.1007/s00013-005-1200-2
  7. Celentani, M. R., Leone, A., Robinson, D. J. S., 10.1016/j.jalgebra.2005.06.002, J. Algebra 301 (2006), 294-307. (2006) Zbl1121.20029MR2230333DOI10.1016/j.jalgebra.2005.06.002
  8. Falco, M. De, Giovanni, F. de, Musella, C., Sysak, Y. P., 10.1090/S0002-9939-2010-10625-1, Proc. Am. Math. Soc. 139 (2011), 385-389. (2011) Zbl1228.20023MR2736322DOI10.1090/S0002-9939-2010-10625-1
  9. Giovanni, F. de, Ialenti, R., 10.1080/00927872.2014.958850, Commun. Algebra 44 (2016), 118-124. (2016) Zbl1344.20045MR3413675DOI10.1080/00927872.2014.958850
  10. Giovanni, F. de, Trombetti, M., 10.1142/S0219498815501431, J. Algebra Appl. 14 (2015), Article ID 1550143, 15 pages. (2015) Zbl1331.20044MR3392592DOI10.1142/S0219498815501431
  11. Giovanni, F. de, Trombetti, M., Wehrfritz, B. A. F., 10.1016/j.jpaa.2022.107185, J. Pure Appl. Algebra 227 (2023), Article ID 107185, 16 pages. (2023) Zbl07584334MR4457897DOI10.1016/j.jpaa.2022.107185
  12. Ferrara, M., Trombetti, M., 10.1007/s00025-022-01734-0, Result. Math. 77 (2022), Article ID 211, 15 pages. (2022) Zbl07595688MR4482267DOI10.1007/s00025-022-01734-0
  13. Franciosi, S., Giovanni, F. de, Groups with many supersoluble subgroups, Ric. Mat. 40 (1991), 321-333. (1991) Zbl0818.20041MR1194163
  14. Hall, P., Higman, G., 10.1112/plms/s3-6.1.1, Proc. Lond. Math. Soc., III. Ser. 6 (1956), 1-42. (1956) Zbl0073.25503MR0072872DOI10.1112/plms/s3-6.1.1
  15. Phillips, R. E., Rainbolt, J. G., 10.1007/s000130050239, Arch. Math. 71 (1998), 97-106. (1998) Zbl0914.20041MR1631464DOI10.1007/s000130050239
  16. Robinson, D. J. S., 10.1007/978-3-662-07241-7, Ergebnisse der Mathematik und ihrer Grenzgebiete 62. Springer, Berlin (1972). (1972) Zbl0243.20032MR0332989DOI10.1007/978-3-662-07241-7
  17. Schmidt, R., 10.1515/9783110868647, De Gruyter Expositions in Mathematics 14. Walter De Gruyter, Berlin (1994). (1994) Zbl0843.20003MR1292462DOI10.1515/9783110868647
  18. Shirvani, M., Wehrfritz, B. A. F., Skew Linear Groups, London Mathematical Society Lecture Note Series 118. Cambridge University Press, Cambridge (1986). (1986) Zbl0602.20046MR0883801
  19. Wehfritz, B. A. F., 10.1016/0021-8693(71)90041-X, J. Algebra 17 (1971), 41-58. (1971) Zbl0206.31302MR0276368DOI10.1016/0021-8693(71)90041-X
  20. Wehfritz, B. A. F., 10.1007/978-3-642-87081-1, Ergebnisse der Mathematik und ihrer Grenzgebiete 76. Springer, Berlin (1973). (1973) Zbl0261.20038MR0335656DOI10.1007/978-3-642-87081-1

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