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I know that the Loewy series of a group can be computed with the help

of a certain central series (Jennings's thm).

Is there either some feature in GAP which determines this series for a

given group or somebody who already wrote a GAP program for that

purpose?

As for p-groups I have written a GAP procedure to compute the Jennings

series of such groups using the fact that it is isomorphic to the

Lazard series L_n(G) = \prod_{ip^j \ge n}\gamma_i(G)^{p^j}. The

calculations are straightforward in GAP.

Furthermore there is a function to test whether a given pc-presentation

for the group is compatible with the Jennings series. In this case

such a presentation can be used (by a theorem of Jennings) to compute

a basis for the group algebra over GF(p), which is compatible with the

Loewy series. This approach has been implemented in the SISYPHOS

program developped in Stuttgart to investigate characteristic p group

algebras of p-groups. It is planned to distribute the program as a

GAP shared library.

Martin Wursthorn

Mathematisches Institut B

Universit"at Stuttgart

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