Finite groups with large Noether number are almost cyclic
نویسندگان
چکیده
منابع مشابه
Finite groups all of whose proper centralizers are cyclic
A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic. In this article we determine all finite $CC$-groups.
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The finite groups having an indecomposable polynomial invariant whose degree is at least half of the order of the group are classified. Apart from four sporadic exceptions these are exactly the groups having a cyclic subgroup of index at most two. The Noether bound is determined for these groups, and estimates are given for various other groups as well.
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In this short note we describe the finite groups G having |G| − 1 cyclic subgroups. This leads to a nice characterization of the symmetric group S3. In subgroup lattice theory, it is a usual technique to associate to a finite group G some posets of subgroups of G (see, e.g., [4]). One such poset is the poset of cyclic subgroups of G, usually denoted by C(G). Notice that there are few papers on ...
متن کاملFinite $p$-groups and centralizers of non-cyclic abelian subgroups
A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
متن کاملThe Noether Numbers for Cyclic Groups of Prime Order
The Noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants. We compute the Noether number for an arbitrary representation of a cyclic group of prime order, and as a consequence prove the “2p− 3 conjecture”.
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ژورنال
عنوان ژورنال: Annales de l'Institut Fourier
سال: 2019
ISSN: 1777-5310
DOI: 10.5802/aif.3280