On Leinster groups of order pqrs
Sekhar Jyoti Baishya

TL;DR
This paper classifies Leinster groups of order p^2qr and proves that no groups of order pqrs are Leinster, providing specific isomorphism types for the former case.
Contribution
It characterizes Leinster groups of order p^2qr and establishes the non-existence of Leinster groups of order pqrs.
Findings
Leinster groups of order p^2qr are isomorphic to Q_{20}×C_{19} or Q_{28}×C_{13}.
No Leinster groups exist of order pqrs.
Provides a complete classification for these specific group orders.
Abstract
A finite group is said to be a Leinster group if the sum of the orders of its normal subgroups equals twice the order of the group itself. Let be primes. We prove that if is a Leinster group of order , then or . We also prove that no group of order is Leinster.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems
