منابع مشابه
POS-groups with some cyclic Sylow subgroups
A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.
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Generalizing a result in the theory of finite fields we prove that, apart from a couple of exceptions that can be classified, for any elements a1, . . . , am of the cyclic group of order m, there is a permutation π such that 1a π(1) + · · ·+maπ(m) = 0.
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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 کاملSubgroups and cyclic groups
Example 1.2. (i) For every group G, G ≤ G. If H ≤ G and H 6= G, we call H a proper subgroup of G. Similarly, for every group G, {1} ≤ G. We call {1} the trivial subgroup of G. Most of the time, we are interested in proper, nontrivial subgroups of a group. (ii) Z ≤ Q ≤ R ≤ C; here the operation is necessarily addition. Similarly, Q∗ ≤ R∗ ≤ C∗, where the operation is multiplication. Likewise, μn ...
متن کاملNotes on Cyclic Groups
is a (abelian) subgroup of G. From this point on we will use the exponent laws without particular reference. The group G is cyclic if G = for some a ∈ G in which case a is said to generate G. Since = for all a ∈ G, if G is cyclic and generated by a then G is also generated by a−1. Suppose that the binary operation of G is written additively. Then the notation n·a, or na, is used i...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1954
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1954.4.481