A note on finite metabelian $p$-groups
نویسندگان
چکیده
منابع مشابه
A Note on Absolute Central Automorphisms of Finite $p$-Groups
Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study some properties of absolute central automorphisms of a given finite $p$-group.
متن کاملA NOTE ON AUTOMORPHISMS OF FINITE p-GROUPS
Let G be a finite non-cyclic p-group of order at least p3. If G has an abelian maximal subgroup, or if G has an elementary abelian centre with CG(Z(Φ(G))) 6= Φ(G), then |G| divides |Aut(G)|.
متن کاملA NOTE ON POLYCYLIC RESIDUALLY FINITE-p GROUPS
A subgroup H of a residually finite-p group G is almost p-closed in G if H has finite p′-index in ̄̄ H, its closure with respect to the pro-p topology on G. We characterise polycyclic residually finite-p groups in which all subgroups are almost p-closed and discuss a few conditions that are sufficient for particular subgroups H to be almost p-closed. We also present, for each prime p, an example...
متن کاملa note on finite c-tidy groups
let $g$ be a group and $x in g$. the cyclicizer of $x$ is defined to be the subset $cyc(x)=lbrace y in g mid langle x, yrangle ; {rm is ; cyclic} rbrace$. $g$ is said to be a tidy group if $cyc(x)$ is a subgroup for all $x in g$. we call $g$ to be a c-tidy group if $cyc(x)$ is a cyclic subgroup for all $x in g setminus k(g)$, where $k(g)$ is the intersection of all the cyclicizers in ...
متن کاملA Note on Beauville p-Groups
We examine which p-groups of order ≤ p6 are Beauville. We completely classify them for groups of order ≤ p4. We also show that the proportion of 2-generated groups of order p5 which are Beauville tends to 1 as p tends to infinity; this is not true, however, for groups of order p6. For each prime p we determine the smallest non-abelian Beauville p-group.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0254132-2