### Abstract

Let q be a prime number. The number of subgroups of order q^{k} in an abelian group G of order q^{n} and type λ is a polynomial in q, [_{k}^{λ′}]_{q}. In 1987, Lynne Butler showed that the first difference, [_{k}^{λ′}] - [_{k - 1}^{λ′}], has nonnegative coefficients as a polynomial in q, when 2k ≤ |λ|. We generalize the first difference to the rth difference, and give conditions for the nonnegativity of its coefficients.

Original language | English (US) |
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Pages (from-to) | 121-137 |

Number of pages | 17 |

Journal | Discrete Mathematics |

Volume | 147 |

Issue number | 1-3 |

DOIs | |

State | Published - Dec 16 1995 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics