## Abstract

Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g→g^{ -1} of G extends linearly to KG; this extension leaves V setwise invariant, and its restriction to V followed by v→v^{ -1} gives an automorphism of V. The elements of V fixed by this automorphism are called unitary; they form a subgroup. Our first theorem describes the K and G for which this subgroup is normal in V. For each element g in G, let {Mathematical expression} denote the sum (in KG) of the distinct powers of g. The elements 1+(g-1) {Mathematical expression} with h,hεG are the bicyclic units of KG. Our second theorem describes the K and G for which all bicyclic units are unitary.

Original language | English |
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Pages (from-to) | 57-72 |

Number of pages | 16 |

Journal | Manuscripta Mathematica |

Volume | 84 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1994 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics