query: $\langle x \rangle$ is a direct summand of a finite abelian group where $x$ is maximal order
positive_passages.docid: 25235
positive_passages.text: Finite abelian groups - direct sum of cyclic subgroup
negative_passages.docid: 127047
negative_passages.text: How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
negative_passages.docid: 36882
negative_passages.text: Two finite abelian groups with the same number of elements of any order are isomorphic
negative_passages.docid: 1990
negative_passages.text: Results for elements in Dihedral Groups: $x \notin \langle r\rangle  \Rightarrow rx = xr^{-1}$
negative_passages.docid: 41731
negative_passages.text: Question about the order of the product of two elements in an abelian group
negative_passages.docid: 81354
negative_passages.text: The product of all the elements of a finite abelian group
negative_passages.docid: 90437
negative_passages.text: Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
negative_passages.docid: 27901
negative_passages.text: Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
negative_passages.docid: 80976
negative_passages.text: Direct Product Of Abelian Group
negative_passages.docid: 83183
negative_passages.text: Why is $\langle x| x' \rangle=\delta(x-x')$?
negative_passages.docid: 145159
negative_passages.text: Finite group is abelian if the representatives of its conjugacy classes commute
negative_passages.docid: 113259
negative_passages.text: The confusing nature of direct sum for finite abelian groups
negative_passages.docid: 7079
negative_passages.text: ord $(b)|\max\{\text{ord}(g)|g\in G\}$ for all $b\in G\,$ a finite abelian group
negative_passages.docid: 89215
negative_passages.text: How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
negative_passages.docid: 108310
negative_passages.text: $(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group