### Abstract

In Frobenius' initial papers on group characters he introduced k-characters in order to give an algorithm to calculate the irreducible factors of the group determinant. We show how his work leads naturally to the construction of a formal power series for any class function on a group, which terminates if and only if the class function is a character. This is then used to obtain a criterion for a class function to be a character.

Original language | English (US) |
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Pages (from-to) | 465-474 |

Number of pages | 10 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 155 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 155, no. 3, pp. 465-474. https://doi.org/10.1017/S0305004113000388

**A formal power series attached to a class function on a group and its application to the characterisation of characters.** / Johnson, Kenneth W.; Poimenidou, Eirini.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A formal power series attached to a class function on a group and its application to the characterisation of characters

AU - Johnson, Kenneth W.

AU - Poimenidou, Eirini

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In Frobenius' initial papers on group characters he introduced k-characters in order to give an algorithm to calculate the irreducible factors of the group determinant. We show how his work leads naturally to the construction of a formal power series for any class function on a group, which terminates if and only if the class function is a character. This is then used to obtain a criterion for a class function to be a character.

AB - In Frobenius' initial papers on group characters he introduced k-characters in order to give an algorithm to calculate the irreducible factors of the group determinant. We show how his work leads naturally to the construction of a formal power series for any class function on a group, which terminates if and only if the class function is a character. This is then used to obtain a criterion for a class function to be a character.

UR - http://www.scopus.com/inward/record.url?scp=85022754879&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85022754879&partnerID=8YFLogxK

U2 - 10.1017/S0305004113000388

DO - 10.1017/S0305004113000388

M3 - Article

AN - SCOPUS:85022754879

VL - 155

SP - 465

EP - 474

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -