Two results on character codegrees
Yang Liu, Yong Yang

TL;DR
This paper investigates properties of character codegrees in finite groups, establishing bounds related to prime divisors and characterizing prime graphs through graph theory, advancing understanding of group structure via character theory.
Contribution
It provides the best bounds for the size of the prime set of a group under specific codegree prime divisor conditions and characterizes codegree prime graphs using graph theory.
Findings
Bounded the size of the prime set for groups with 2, 3, and 4 prime divisors in codegrees.
Characterized codegree prime graphs for certain groups purely through graph properties.
Abstract
Let be a finite group and be the set of irreducible characters of . The codegree of an irreducible character of the group is defined as . In this paper, we study two topics related to the character codegrees. Let be the maximal integer such that there is a member in having distinct prime divisors, where . One is related to the codegree version of the Huppert's - conjecture and we obtain the best possible bound for under the condition and respectively. The other is related to the prime graph of character codegrees and we show that the codegree prime graphs of several classes of groups can be characterized only by graph theoretical terms.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Cooperative Communication and Network Coding
