We study Shunkov groups with the following condition: the normalizer of any finite nontrivial subgroup has an almost layer-finite periodic part. Under this condition, we establish the structure of Sylow 2-subgroups in this group.
Similar content being viewed by others
References
S. I. Adyan, Burnside Problem and Identities in Groups [in Russian], Nauka, Moscow (1975).
A. Yu. Ol’shanskii, Geometry of Defining Relations in Groups [in Russian], Nauka, Moscow (1989).
S. N. Chernikov, “On the theory of infinite p-groups,” Dokl. Akad. Nauk SSSR, 71–74 (1945).
V. I. Senashov, “Structure of an infinite Sylow subgroup in some Shunkov groups,” Vest. Sib. Gos. A´erokosm. Univ., Issue 1(47), 74–79 (2013).
V. I. Senashov, “Sufficient conditions for the almost layer finiteness of groups,” Ukr. Mat. Zh., 51, No. 4, 472–485 (1999); English translation: Ukr. Math. J., No. 4, 525–537 (1999).
V. I. Senashov, “Structure of an infinite Sylow subgroup in some periodic Shunkov groups,” Diskr. Mat., 14, No. 4, 133–152 (2002).
V. I. Senashov, “On Shunkov groups with strongly imbedded subgroup,” Tr. Inst. Mat. Mekh. Ural. Otdel. Ros. Akad. Nauk, 15, No. 2, 203–210 (2009).
V. I. Senashov, “On Shunkov groups with strongly imbedded almost layer-finite subgroup,” Tr. Inst. Mat. Mekh. Ural. Otdel. Ros. Akad. Nauk, 16, No. 3, 234–239 (2010).
V. I. Senashov, “On groups with a strongly imbedded subgroup having an almost layer-finite periodic part,” Ukr. Mat. Zh., 64, No. 3, 384–391 (2012); English translation: Ukr. Math. J., 64, No. 3, 433–440 (2012).
V. I. Senashov, “Groups satisfying the minimality condition for non-almost-layer-finite subgroups,” Ukr. Mat. Zh., 43, No. 7–8, 1002–1008 (1991); English translation: Ukr. Math. J., 43, No. 7–8, 935–941 (1991).
V. I. Senashov, “Almost layer finiteness of a periodic group without involutions,” Ukr. Mat. Zh., 51, No. 11, 1529–1533 (1999); English translation: Ukr. Math. J., 51, No. 11, 1729–1732 (1999).
V. I. Senashov, “On Sylow subgroups of Shunkov periodic groups,” Ukr. Mat. Zh., 57, No. 11, 1548–1556 (2005); English translation: Ukr. Math. J., 57, No. 11, 1809–1817 (2005).
V. I. Senashov and V. P. Shunkov, “Almost layer finiteness of the periodic part of a group without involutions,” Diskr. Mat., 15, No. 3, 91–104 (2003).
V. P. Shunkov, On the Embedding of Primary Elements in a Group [in Russian], Nauka, Novosibirsk (1992).
M. Hall, Jr., The Theory of Groups [Russian translation], Inostr. Literatura, Moscow (1962).
V. P. Shunkov, “On the problem of minimality for locally finite groups,” Algebra Logika, 9, No. 2, 220–248 (1970).
V. P. Shunkov, “On periodic groups with certain conditions of finiteness,” Dokl. Akad. Nauk SSSR, 195, No. 6, 1290–1293 (1970).
G. A. Malan’ina, “Semidirect products of cyclic groups,” Dokl. Akad. Nauk SSSR, 132, 762–765 (1960).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 3, pp. 397–405, March, 2015.\\
Rights and permissions
About this article
Cite this article
Senashov, V.I. On Sylow Subgroups of Some Shunkov Groups. Ukr Math J 67, 455–463 (2015). https://doi.org/10.1007/s11253-015-1092-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-015-1092-2