# Groups with exactly two supercharacter theories

@article{Burkett2015GroupsWE, title={Groups with exactly two supercharacter theories}, author={Shawn Tyler Burkett and Jonathan P. Lamar and Mark L. Lewis and Casey Wynn}, journal={Communications in Algebra}, year={2015}, volume={45}, pages={977 - 982} }

ABSTRACT In this paper, we classify those finite groups with exactly two supercharacter theories. We show that the solvable groups with two supercharacter theories are ℤ3 and S3. We also show that the only nonsolvable group with two supercharacter theories is Sp(6,2).

#### 13 Citations

Towards the classification of finite simple groups with exactly three or four supercharacter theories

- Mathematics
- Asian-European Journal of Mathematics
- 2018

A supercharacter theory for a finite group [Formula: see text] is a set of superclasses each of which is a union of conjugacy classes together with a set of sums of irreducible characters called… Expand

Supercharacter theories of dihedral groups

- Mathematics
- 2016

The set of supercharacter theories of a fixed group $G$ forms a natural lattice. An open question in the study of supercharacter theories is to classify this lattice, and to date, this has only been… Expand

An algorithm for constructing all supercharacter theories of a finite group

- Computer Science, Mathematics
- Ars Math. Contemp.
- 2020

An algorithm for constructing supercharacter theories of a finite group by which all super character theories of groups containing up to 14 conjugacy classes are calculated is introduced. Expand

Counting the number of supercharacter theories of a finite group

- Mathematics
- Comptes Rendus Mathematique
- 2019

Abstract The supercharacter theory of a finite group is a generalization of the ordinary character theory of finite groups that was introduced by Diaconis and Isaacs in 2008. In this paper, the… Expand

Supercharacter theories of semiextraspecial p-groups and Frobenius groups

- Mathematics
- Journal of Algebra
- 2018

Abstract In this paper, we describe all supercharacter theories of semiextraspecial p-groups and Frobenius groups. We first review the constructions which will classify these supercharacter theories.… Expand

Supercharacters of Unipotent and Solvable Groups

- Mathematics
- Journal of Mathematical Sciences
- 2018

The notion of the supercharacter theory was introduced by P. Diaconis and I. M. Isaaks in 2008. In this paper, we present a review of the main notions and facts of the general theory and discuss the… Expand

The structure of normal lattice supercharacter theories

- Mathematics
- 2018

The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product… Expand

Finding supercharacter theories on character tables

- Mathematics
- 2020

Abstract We describe an easy way how to find supercharacter theories for a finite group, if its character table is known. Namely, we show how an arbitrary partition of the conjugacy classes or of the… Expand

Groups with One or Two Super-Brauer Character Theories

- Mathematics
- 2017

A super-Brauer character theory of a group G and a prime p is a pair consisting of a partition of the irreducible p -Brauer characters and a partition of the p -regular elements of G that satisfy… Expand

Projective supercharacter theory

- Mathematics
- 2020

Abstract The idea of supercharacters for ordinary characters of a finite group G was introduced by Diaconis and Isaacs and further extended to Brauer characters by Chen and Lewis. The twin concepts… Expand

#### References

SHOWING 1-10 OF 12 REFERENCES

Supercharacter Theories Constructed by the Method of Little Groups

- Mathematics
- 2014

The “method of little groups” describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this… Expand

Supercharacter Theory Constructions Corresponding to Schur Ring Products

- Mathematics
- 2012

Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain approximations to the ordinary character theory of the group [7]. We make explicit the connection between… Expand

Supercharacters and superclasses for algebra groups

- Mathematics
- 2007

We study certain sums of irreducible characters and compatible unions of conjugacy classes in finite algebra groups. These groups generalize the unimodular upper triangular groups over a finite… Expand

On Schur Rings over Cyclic Groups, II

- Mathematics
- 1996

In this paper, we introduce the notion of wedge product of Schur rings. We show that for any nontrivial Schur ringS over a cyclic groupG, if there is a subgroupH such that Σg eHg Σg∈Hg ∉S, thenS is… Expand

On schur rings over cyclic groups

- Mathematics
- 1998

In this paper, we introduce the notion of wedge product of Schur rings. We show that for any nontrivial Schur ringS over a cyclic groupG, if there is a subgroupH such that Σg εHg Σg∈Hg ∉S, thenS is… Expand

Fusions of Character Tables and Schur Rings of Abelian Groups

- Mathematics
- 2008

If the character table of a finite group H satisfies certain conditions, then the classes and characters of H can fuse to give the character table of a group G of the same order. We investigate the… Expand

Character Theory of Finite Groups

- Mathematics
- 2010

1. (i) Suppose K is a conjugacy class of Sn contained in An; then K is called split if K is a union of two conjugacy classes of An. Show that the number of split conjugacy classes contained in An is… Expand

The Sage Developers

- Sage Mathematics So ware
- 2015

Supercharacter Theories of Finite Cyclic Groups

- Ph. D. Dissertation,
- 2008