
TL;DR
This paper characterizes certain odd-order p-groups called Schur groups, proving specific structures are Schur and classifying all noncyclic Schur p-groups for odd primes.
Contribution
It proves that groups of the form Z_3 × Z_{3^n} are Schur and classifies all noncyclic Schur p-groups for odd primes.
Findings
Groups Z_3 × Z_{3^n} are Schur.
All noncyclic Schur p-groups for odd p are either Z_3 × Z_3 × Z_3 or Z_3 × Z_{3^n}.
Provides a classification of certain Schur p-groups.
Abstract
A finite group is called a Schur group if any -ring over is associated in a natural way with a subgroup of that contains all right translations. We prove that the groups , where , are Schur. Modulo previously obtained results, it follows that every noncyclic Schur -group, where is an odd prime, is isomorphic to or , .
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