Large 2-groups of automorphisms of algebraic curves over a field of characteristic 2. Massimo, G. and Gábor, K. JOURNAL OF ALGEBRA, 427:264--294, 2015.
Large 2-groups of automorphisms of algebraic curves over a field of characteristic 2 [link]Paper  doi  abstract   bibtex   
Let S be a 2-subgroup of the K-automorphism group Aut(X) of an algebraic curve X of genus g(X) defined over an algebraically closed field K of characteristic 2. It is known that S may be quite large compared to the classical Hurwitz bound 84(g(X)−1). However, if S fixes no point, then the size of S is smaller than or equal to 4(g(X)−1). In this paper, we investigate algebraic curves X with a 2-subgroup S of Aut(X) having the following properties: (I) |S|≥8 and |S|>2(g(X)−1), (II) S fixes no point on X. Theorem 1.2 shows that X is a general curve and that either |S|=4(g(X)−1), or |S|=2g(X)+2, or, for every involution u∈Z(S), the quotient curve X/〈u〉 inherits the above properties, that is, it has genus ≥2, and its automorphism group S/〈u〉 still has properties (I) and (II). In the first two cases, S is completely determined. We also give examples illustrating our results. In particular, for every g=2h+1≥9, we exhibit a (general bielliptic) curve X of genus g whose K-automorphism group has a dihedral 2-subgroup S of order 4(g−1) that fixes no point in X.
@article{
	11391_1344516,
	author = { Giulietti  Massimo  and  Korchmáros  Gábor },
	title = {Large 2-groups of automorphisms of algebraic curves over a field of characteristic 2},
	year = {2015},
	journal = {JOURNAL OF ALGEBRA},
	volume = {427},
	abstract = {Let S   be a 2-subgroup of the K-automorphism group Aut(X) of an algebraic curve X of genus g(X) defined over an algebraically closed field K of characteristic 2. It is known that S   may be quite large compared to the classical Hurwitz bound 84(g(X)−1). However, if S fixes no point, then the size of S   is smaller than or equal to 4(g(X)−1). In this paper, we investigate algebraic curves X with a 2-subgroup S   of Aut(X) having the following properties:

(I)
|S|≥8 and |S|>2(g(X)−1),
(II)
S   fixes no point on X.
Theorem 1.2 shows that X is a general curve and that either |S|=4(g(X)−1), or |S|=2g(X)+2, or, for every involution u∈Z(S), the quotient curve X/〈u〉 inherits the above properties, that is, it has genus ≥2, and its automorphism group S/〈u〉 still has properties (I) and (II). In the first two cases, S   is completely determined. We also give examples illustrating our results. In particular, for every g=2h+1≥9, we exhibit a (general bielliptic) curve X of genus g whose K-automorphism group has a dihedral 2-subgroup S   of order 4(g−1) that fixes no point in X.},
	keywords = {Algebraic curves, Positive characteristic, Automorphism groups},
	url = {http://www.sciencedirect.com/science/article/pii/S0021869314007182},
	doi = {10.1016/j.jalgebra.2014.12.019},	
	pages = {264--294}
}
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