TY - JOUR

T1 - Pronormality and Submaximal X -Subgroups on Finite Groups

T2 - Dedicated to celebrate the Sixtieth anniversary of USTC

AU - Guo, Wenbin

AU - Revin, Danila O.

N1 - Publisher Copyright: © 2018, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - According to Hall, a subgroup H of a group G is said to be pronormal if H and Hg are conjugate in ⟨ H, Hg⟩ for every g∈ G. In this survey, we discuss the role of pronormality for some subgroups of finite groups: Hall subgroups, subgroups of odd index, submaximal X-subgroup, etc.

AB - According to Hall, a subgroup H of a group G is said to be pronormal if H and Hg are conjugate in ⟨ H, Hg⟩ for every g∈ G. In this survey, we discuss the role of pronormality for some subgroups of finite groups: Hall subgroups, subgroups of odd index, submaximal X-subgroup, etc.

KW - Hall π-subgroup

KW - Pronormal subgroup

KW - Subgroup of odd index

KW - Submaximal X-subgroup

KW - EXISTENCE

KW - Hall pi-subgroup

KW - ISOMORPHISM-PROBLEM

KW - PRIMITIVE PERMUTATION-GROUPS

KW - HALL SUBGROUPS

KW - ODD INDEX

KW - CRITERION

KW - Submaximal (sic)-subgroup

KW - CONJUGACY

UR - http://www.scopus.com/inward/record.url?scp=85053202701&partnerID=8YFLogxK

U2 - 10.1007/s40304-018-0154-9

DO - 10.1007/s40304-018-0154-9

M3 - Article

AN - SCOPUS:85053202701

VL - 6

SP - 289

EP - 317

JO - Communications in Mathematics and Statistics

JF - Communications in Mathematics and Statistics

SN - 2194-6701

IS - 3

ER -