Coclass theory
Bettina Eick
Coclass theory has been one of my main research projects for many years.
It started as an approach towards a new classification for finite p-groups.
Meanwhile, similar ideas has been tried for nilpotent Lie algebras and
nilpotent associative algebras. Below are my main publications in these
areas.
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Coclass Theory for finite p-Groups
- On the classification of prime-power groups
by coclass. With Charles Leedham-Green. Bull. Lond.
Math. Soc. 40, 274 -- 288 (2008)
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On the classification of groups of prime-power order by coclass:
The 3-groups of coclass 2. With C.R. Leedham-Green,
M.F. Newman and E.A. O'Brien.
J. Algebra Comput. 23, 1243 -- 1288 (2013).
- On the number of infinite branches in the
graph of all p-groups of coclass r. J. Group Theory 8, 687 - 700
(2005)
- On the determination of the uniserial space
groups with a given coclass. J. London Math. Soc. (2) 71,
622 - 642 (2005)
- Schur multiplicators of finite p-groups
with fixed coclass. Israel J. Math. 166, 157 -- 166 (2008)
- Schur multiplicators of infinite pro-p-groups
with finite coclass. Israel J. Math. 166, 147 -- 156 (2008)
- Automorphism groups of 2-groups.
J. Algebra (Comput. Sec.) 300, 91 -- 101 (2006)
- On p-groups of maximal class with 'large'
automorphism group. With H. Dietrich.
J. Group Theory 20, 227 -- 256 (2017).
- Metabelian p-groups and coclass theory
J. Algebra 421, 102 -- 118 (2014).
- Computation of low-dimensional (co)homology
groups for infinite sequences of p-groups with fixed coclass.
With D. Feichtenschlager. IJAC 21(4), 635--649 (2011)
- Investigating p-groups by coclass with GAP.
With H. Dietrich and D. Feichtenschlager. In Proceedings
`AMS Special Session on Computational Group Theory' by Kappe, Magidin
and Morse, AMS Contemp. Math. 470, 45 -- 61 (2008)
- Cochain sequences and the Quillen category of
a coclass family. With D. Green.
J. Australian Math. Soc. 102, 185 -- 204 (2017)
- The Quillen categories of $p$-groups and
coclass theory. With D. Green.
Israel J. Math. 206, 183 -- 212 (2015).
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The class-breadth conjecture revisited. With M. Newman and
E.A.O'Brien J. Algebra 300, 384 -- 393 (2006).
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On efficient presentations for infinite families of 2-groups with
fixed coclass. With H. Abdolzadeh.
Algebra Colloquium 20, 561 -- 572 (2013).
Coclass Theory for Nilpotent Associative Algebras
- Classifying nilpotent associative algebras:
small coclass and finite fields.
With T. Moede. In Proceedings: Algorithmic and experimental
methods in algebra, geometry, and number theory. Springer (ISBN
978-3-319-70565-1 and 978-3-319-70566-8), 213 -- 229 (2017).
- Coclass theory for finite nilpotent associative
algebras: Algorithms and a periodicity conjecture.
With T. Moede. Exp. Math. 26, 267 -- 274 (2017)
- Nilpotent associative algebras and coclass
theory. With T. Moede. J. Algebra 434, 249 -- 260
(2015)
- Coclass theory for nilpotent semigroups via
their associated algebras. With Andreas Distler.
J. Algebra 373, 491 -- 501 (2013).
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