## Abstract

We establish and comment on a surprising relationship between the behaviour modulo a prime p of the number s_{n} (G) of index n subgroups in a group G, and that of the corresponding subgroup numbers for a subnormal subgroup of p-power index in G. One of the applications of this result presented here concerns the explicit determination modulo p of s_{n} (G) in the case when G is the fundamental group of a finite graph of finite p-groups. As another application, we extend one of the main results of the second author's paper (Forum Math, in press) concerning the p-patterns of free powers G* q of a finite group G with q a p-power to groups of the more general form H* G*^{q}, where H is any finite p-group.

Original language | English |
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Pages (from-to) | 189-203 |

Number of pages | 15 |

Journal | Journal of Pure and Applied Algebra |

Volume | 203 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1 Dec 2005 |