TY - JOUR
AU - Yang, Xu
AB - In this paper, the author characterizes the subgroups of a finite metacyclic group K by building a one to one correspondence between certain 3-tuples (k,l,β) ∈ ℕ3 and all the subgroups of K. The results are applied to compute some subgroups of K as well as to study the structure and the number of p-subgroups of K, where p is a fixed prime number. In addition, the author gets a factorization of K, and then studies the metacyclic p-groups, gives a different classification, and describes the characteristic subgroups of a given metacyclic p-group when p ≥ 3. A “reciprocity” relation on enumeration of subgroups of a metacyclic group is also given.
TI - The Subgroups of Finite Metacyclic Groups
JF - Chinese Annals of Mathematics - Series B
DO - 10.1007/s11401-020-0197-6
DA - 2020-03-03
UR - https://www.deepdyve.com/lp/springer-journals/the-subgroups-of-finite-metacyclic-groups-qyeV0UlFpU
SP - 241
EP - 266
VL - 41
IS - 2
DP - DeepDyve
ER -