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On Friday Mar. 8th 2002, Igor Schein asked about GAP SmallGroup(40,3).

Using g4003 and similar abbreviations, g4003 has generators (a^5=b^8=1,

ba=aab), with the second part being a non-abelian re-write rule. It has

g2001 (Q20, with a^5=b^4=1, ba=aaaab) as a subgroup, and g2003 (with

a^5=b^4=1, ba=aab) as a factor (quotient) group. The CayleyTable determinant

has two linear factors, one quadratic factor, one unrepeated fourth order

and two fourth order factors that are each repeated four times.

Similar groups:- g2401 is (a^3=b^8=1, ba=aab), g4001 is (a^5=b^8=1,

ba=aaaab), g4007 is (a^5=b^4=c^2=1, ba=aaaab), g4012 is (a^5=b^4=c^2=1,

ba=aab), g4013 is (a^5=b^2=c^2=d^2=1, ba=aaaab), g5601 is (a^7=b^8=1,

ba=aaaaaab), g7201 is (a^9=b^8=1, ba=aaaaaaaab), and g10403 is (a^13=b^8=1,

ba=aaaaab). I have not looked at 88-element groups; other rewrite rules give

the same groups, or non-associative tables, with my procedure.

This information was obtained in a few minutes investigation using my

Mathematica "concast.ma" package, after transcribing g10403 from a GAP

session. it took 1040 secs (on a 700mHz PC) to find and identify the g10403

subgroups as {{1, "C2"}, {13, "C4"}, {13, "C8"}, {1, "C13"}, {1, "C26"}}.

This package is mainly concerned with conservative Cayley tables as

multiplication rules for renormalizing algebras, but includes a database of

groups (primarily with less than 73 elements) and procedures to generate,

investigate, and identify them.Contact me at

mail@beresford22.freeserve.com.uk if you would like a (600kb) Mathematica

demonstration notebook that includes the package.

Roger Beresford.

Miles-Receive-Header: reply

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