TY - JOUR
ID - 45109
TI - Some Structural Properties of Upper and Lower Central Series of Pairs of Groups
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Kaheni, Azam
AU - Kayvanfar, Saeed
AD - Ferdowsi University of Mashhad
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Y1 - 2018
PY - 2018
VL - 3
IS - 2
SP - 99
EP - 108
KW - n-Isoclinism
KW - pair of groups
KW - Quotient irreducible pair
KW - pi-groups
DO - 10.22052/mir.2017.56003.1035
N2 - In this paper, we first present some properties of lower and upper central series of pair of groups. Then the notion of $n$-isoclinism for the classification of pairs of groups is introduced, and some of the structural properties of the created classes are proved. Moreover some interesting theorems such as Baer Theorem, Bioch Theorem, Hirsh Theorem for pair of groups are generalized. Finally, it is shown that each $n$-isoclinism family of pairs contains a quotient irreducible pair.
UR - http://mir.kashanu.ac.ir/article_45109.html
L1 - http://mir.kashanu.ac.ir/article_45109_b22684cd6fd03b64d74b22ff07832283.pdf
ER -