Finding central decompositions of p-groups

Details Finding central decompositions of p-groups Finding central decompositions of p-groups

2008-01-22

arxiv.org/abs/0801.3434v2

J. Group Theory 12 (2009), 813--830

Mathematics

Group Theory

28 pages

Scientific paper

10.1515/JGT.2009.015

Polynomial-time algorithms are given to find a central decomposition of maximum size for a finite p-group of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las Vegas probabilistic routines to compute the structure of finite *-rings and also the Las Vegas C-MeatAxe. When p is small, the probabilistic methods can be replaced by deterministic polynomial-time algorithms. The methods introduce new group isomorphism invariants including new characteristic subgroups.

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