Date of Award
2020
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Poimenidou, Eirini
Area of Concentration
Mathematics
Abstract
In this thesis, we examine the normal power graph of certain classes of finite groups. For a finite group G with normal subgroup N, the normal power graph of G, denoted by rN(G), is a graph with vertex set (G−N)u{e}, and two distinct vertices x and y are adjacent if xN = ymN or xnN = yN for some m,n EN. We compute the normal power graph of the general metacyclic group with respect to its kernel. We also prove that if a group G is equal to HN for some H 6 G and N /G, G = N oH if and only if r∗ N(G) ∼ = K|N| r∗(H); we also prove that if N /G and H is a Hall subgroup of G, G = N o H if and only if r∗ N(G) ∼ = K|N| r∗(H). Finally, we compute the proper normal power graph of the direct product of two groups using generalized products.
Recommended Citation
Bogart, Fiona, "NORMAL POWER GRAPHS OF FINITE GROUPS" (2020). Theses & ETDs. 5907.
https://digitalcommons.ncf.edu/theses_etds/5907