### Abstract

Let G be a finite group and A(G) the Burnside ring of G. The family of rings A(H), where H ranges over the set of all proper subgroups of G, yields the inverse limit L(G) and a canonical homomorphism from A(G) to L(G) which is called the restriction map. Let Q(G) be the cokernel of this homomorphism. It is known that Q(G) is a finite abelian group and is isomorphic to the cartesian product of Q(G/N(p)), where p runs over the set of primes dividing the order of G and N(p) stands for the smallest normal subgroup of G such that the order of G/N(p) is a power of p. Therefore, it is important to investigate Q(G) for G of prime power order. In this paper we develop a way to compute Q(G) for cartesian products G of two cyclic p-groups.

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

Pages (from-to) | 95-105 |

Number of pages | 11 |

Journal | Kyushu Journal of Mathematics |

Volume | 72 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Burnside ring
- Finite group
- Inverse limit

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Cokernels of homomorphisms from burnside rings to inverse limits II : G = C _{pm } × C_{pn }.** / Morimoto, Masaharu; Sugimura, Masafumi.

Research output: Contribution to journal › Article

_{pm }× C

_{pn }',

*Kyushu Journal of Mathematics*, vol. 72, no. 1, pp. 95-105. https://doi.org/10.2206/kyushujm.72.95

}

TY - JOUR

T1 - Cokernels of homomorphisms from burnside rings to inverse limits II

T2 - G = Cpm × Cpn

AU - Morimoto, Masaharu

AU - Sugimura, Masafumi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let G be a finite group and A(G) the Burnside ring of G. The family of rings A(H), where H ranges over the set of all proper subgroups of G, yields the inverse limit L(G) and a canonical homomorphism from A(G) to L(G) which is called the restriction map. Let Q(G) be the cokernel of this homomorphism. It is known that Q(G) is a finite abelian group and is isomorphic to the cartesian product of Q(G/N(p)), where p runs over the set of primes dividing the order of G and N(p) stands for the smallest normal subgroup of G such that the order of G/N(p) is a power of p. Therefore, it is important to investigate Q(G) for G of prime power order. In this paper we develop a way to compute Q(G) for cartesian products G of two cyclic p-groups.

AB - Let G be a finite group and A(G) the Burnside ring of G. The family of rings A(H), where H ranges over the set of all proper subgroups of G, yields the inverse limit L(G) and a canonical homomorphism from A(G) to L(G) which is called the restriction map. Let Q(G) be the cokernel of this homomorphism. It is known that Q(G) is a finite abelian group and is isomorphic to the cartesian product of Q(G/N(p)), where p runs over the set of primes dividing the order of G and N(p) stands for the smallest normal subgroup of G such that the order of G/N(p) is a power of p. Therefore, it is important to investigate Q(G) for G of prime power order. In this paper we develop a way to compute Q(G) for cartesian products G of two cyclic p-groups.

KW - Burnside ring

KW - Finite group

KW - Inverse limit

UR - http://www.scopus.com/inward/record.url?scp=85049176720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049176720&partnerID=8YFLogxK

U2 - 10.2206/kyushujm.72.95

DO - 10.2206/kyushujm.72.95

M3 - Article

AN - SCOPUS:85049176720

VL - 72

SP - 95

EP - 105

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

SN - 1340-6116

IS - 1

ER -