### Abstract

Brauer's induction theorem, published in 1951, asserts that every element of the complex representation ring R(G) of a finite group G is a linear combination of classes induced from 1-dimensional representations of subgroups of G. In 1987, Snaith formulated an explicit version of the induction theorem. Using the methods of equivariant fibrewise stable homotopy theory, specifically fixed-point theory, this note clarifies the relation between the explicit Brauer induction theorem due to Snaith, Boltje and Symonds and a topological splitting theorem established by Segal in 1973.

Original language | English |
---|---|

Pages (from-to) | 469-475 |

Number of pages | 6 |

Journal | Archiv der Mathematik |

Volume | 77 |

DOIs | |

Publication status | Published - 2001 |

### Cite this

*Archiv der Mathematik*,

*77*, 469-475. https://doi.org/10.1007/PL00000519

**Brauer Induction and Equivariant Stable Homotopy.** / Crabb, Michael Charles.

Research output: Contribution to journal › Article

*Archiv der Mathematik*, vol. 77, pp. 469-475. https://doi.org/10.1007/PL00000519

}

TY - JOUR

T1 - Brauer Induction and Equivariant Stable Homotopy

AU - Crabb, Michael Charles

PY - 2001

Y1 - 2001

N2 - Brauer's induction theorem, published in 1951, asserts that every element of the complex representation ring R(G) of a finite group G is a linear combination of classes induced from 1-dimensional representations of subgroups of G. In 1987, Snaith formulated an explicit version of the induction theorem. Using the methods of equivariant fibrewise stable homotopy theory, specifically fixed-point theory, this note clarifies the relation between the explicit Brauer induction theorem due to Snaith, Boltje and Symonds and a topological splitting theorem established by Segal in 1973.

AB - Brauer's induction theorem, published in 1951, asserts that every element of the complex representation ring R(G) of a finite group G is a linear combination of classes induced from 1-dimensional representations of subgroups of G. In 1987, Snaith formulated an explicit version of the induction theorem. Using the methods of equivariant fibrewise stable homotopy theory, specifically fixed-point theory, this note clarifies the relation between the explicit Brauer induction theorem due to Snaith, Boltje and Symonds and a topological splitting theorem established by Segal in 1973.

U2 - 10.1007/PL00000519

DO - 10.1007/PL00000519

M3 - Article

VL - 77

SP - 469

EP - 475

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

ER -