On the character degree graph of solvable groups
نویسندگان
چکیده
منابع مشابه
Character Sheaves on Neutrally Solvable Groups
Let G be an algebraic group over an algebraically closed field k of characteristic p > 0. In this paper we develop the theory of character sheaves on groups G such that their neutral connected components G◦ are solvable algebraic groups. For such algebraic groups G (which we call neutrally solvable) we will define the set CS(G) of character sheaves on G as certain special (isomorphism classes o...
متن کاملSolvable groups whose character degree graphs have non-trivial fundamental groups
In this talk, we introduce the character degree graph of a finite group G. We will discuss various properties of this graph, and we will further discuss what graphs can occur as the character degree graphs of finite solvable groups. In particular, we focus on groups with characters of degree pq, pr, and qr, where p, q, and r are distinct primes. Although some group theory will be assumed, knowl...
متن کاملON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...
متن کاملOn the Average Character Degree of Finite Groups
We prove that if the average of the degrees of the irreducible characters of a finite group G is less than 16/5, then G is solvable. This solves a conjecture of I. M. Isaacs, M. Loukaki and the first author. We discuss related questions.
متن کاملGroups with a Character of Large Degree
Let G be a finite group of order n and V a simple C[G]-module of dimension d. For some nonnegative number e, we have n = d(d + e). If e is small, then the character of V has unusually large degree. We fix e and attempt to classify such groups. For e ≤ 3 we give a complete classification. For any other fixed e we show that there are only finitely many examples.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13879