Conjugacy of Maximal and Submaximal 픛-Subgroups

Standard

Conjugacy of Maximal and Submaximal 픛-Subgroups. / Guo, W.; Revin, D. O.

In: Algebra and Logic, Vol. 57, No. 3, 01.07.2018, p. 169-181.

Research output: Contribution to journal › Article › peer-review

Harvard

Guo, W & Revin, DO 2018, 'Conjugacy of Maximal and Submaximal 픛-Subgroups', Algebra and Logic, vol. 57, no. 3, pp. 169-181. https://doi.org/10.1007/s10469-018-9490-9

APA

Guo, W., & Revin, D. O. (2018). Conjugacy of Maximal and Submaximal 픛-Subgroups. Algebra and Logic, 57(3), 169-181. https://doi.org/10.1007/s10469-018-9490-9

Vancouver

Guo W, Revin DO. Conjugacy of Maximal and Submaximal 픛-Subgroups. Algebra and Logic. 2018 Jul 1;57(3):169-181. doi: 10.1007/s10469-018-9490-9

Author

Guo, W. ; Revin, D. O. / Conjugacy of Maximal and Submaximal 픛-Subgroups. In: Algebra and Logic. 2018 ; Vol. 57, No. 3. pp. 169-181.

BibTeX

@article{f781cc1bd4ec4bc7a056e9e9833d755c,

title = "Conjugacy of Maximal and Submaximal 픛-Subgroups",

abstract = "Let 픛 be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Following H. Wielandt, we call a subgroup H of a finite group G a submaximal 픛-subgroup if there exists an isomorpic embedding ϕ: G ↪ G* of the group G into some finite group G* under which Gϕ is subnormal in G* and Hϕ = K ∩Gϕ for some maximal 픛-subgroup K of G*. We discuss the following question formulated by Wielandt: Is it always the case that all submaximal 픛-subgroups are conjugate in a finite group G in which all maximal 픛-subgroups are conjugate? This question strengthens Wielandt{\textquoteright}s known problem of closedness for the class of [InlineMediaObject not available: see fulltext.]-groups under extensions, which was solved some time ago. We prove that it is sufficient to answer the question mentioned for the case where G is a simple group.",

keywords = "finite group, Hall π-subgroup, maximal 𝔛-subgroup, submaximal 𝔛-subgroup, [InlineMediaObject not available: see fulltext.]-property, Hall p-subgroup, Dpproperty, DX-property., maximal X-subgroup, HALL SUBGROUPS, FINITE-GROUPS, submaximal X-subgroup",

author = "W. Guo and Revin, {D. O.}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2018",

month = jul,

day = "1",

doi = "10.1007/s10469-018-9490-9",

language = "English",

volume = "57",

pages = "169--181",

journal = "Algebra and Logic",

issn = "0002-5232",

publisher = "Springer US",

number = "3",

}

RIS

TY - JOUR

T1 - Conjugacy of Maximal and Submaximal 픛-Subgroups

AU - Guo, W.

AU - Revin, D. O.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - Let 픛 be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Following H. Wielandt, we call a subgroup H of a finite group G a submaximal 픛-subgroup if there exists an isomorpic embedding ϕ: G ↪ G* of the group G into some finite group G* under which Gϕ is subnormal in G* and Hϕ = K ∩Gϕ for some maximal 픛-subgroup K of G*. We discuss the following question formulated by Wielandt: Is it always the case that all submaximal 픛-subgroups are conjugate in a finite group G in which all maximal 픛-subgroups are conjugate? This question strengthens Wielandt’s known problem of closedness for the class of [InlineMediaObject not available: see fulltext.]-groups under extensions, which was solved some time ago. We prove that it is sufficient to answer the question mentioned for the case where G is a simple group.

AB - Let 픛 be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Following H. Wielandt, we call a subgroup H of a finite group G a submaximal 픛-subgroup if there exists an isomorpic embedding ϕ: G ↪ G* of the group G into some finite group G* under which Gϕ is subnormal in G* and Hϕ = K ∩Gϕ for some maximal 픛-subgroup K of G*. We discuss the following question formulated by Wielandt: Is it always the case that all submaximal 픛-subgroups are conjugate in a finite group G in which all maximal 픛-subgroups are conjugate? This question strengthens Wielandt’s known problem of closedness for the class of [InlineMediaObject not available: see fulltext.]-groups under extensions, which was solved some time ago. We prove that it is sufficient to answer the question mentioned for the case where G is a simple group.

KW - finite group

KW - Hall π-subgroup

KW - maximal 𝔛-subgroup

KW - submaximal 𝔛-subgroup

KW - [InlineMediaObject not available: see fulltext.]-property

KW - Hall p-subgroup

KW - Dpproperty

KW - DX-property.

KW - maximal X-subgroup

KW - HALL SUBGROUPS

KW - FINITE-GROUPS

KW - submaximal X-subgroup

UR - http://www.scopus.com/inward/record.url?scp=85054182700&partnerID=8YFLogxK

U2 - 10.1007/s10469-018-9490-9

DO - 10.1007/s10469-018-9490-9

M3 - Article

AN - SCOPUS:85054182700

VL - 57

SP - 169

EP - 181

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -

ID: 16956456