Question

Given that $G$ is subdirect product of $A$ and $B,$ and $G/G'$ is not subdirect product of $A/A'$ and $ B/B',$ this group contains $G'$?

score 157 · Answer 1 · 2026-03-26 19:19:59

157

Views

Given that $G$ is subdirect product of $A$ and $B,$ and $G/G'$ is not subdirect product of $A/A'$ and $ B/B',$ this group contains $G'$?

Published on 26 Mar 2026 - 19:19

score 62 · Answer 2 · 2016-12-21 13:41:01

62

Views

Does this limit with a Product Exist?

Published on 21 Dec 2016 - 13:41

score 307 · Answer 3 · 2026-03-27 00:06:02

307

Views

About $\prod_{n\in\mathbb Z}\left[{\tanh\Big(\frac{\pi}{2}\sqrt{a^2n^2+ab}\Big)\over\tanh\Big(\frac{\pi}{2}\sqrt{n^2/a^2+b/a}\Big)}\right]^{(-1)^n}=1$

Published on 27 Mar 2026 - 0:06

score 83 · Answer 4 · 2016-12-23 16:33:49

83

Views

Derivative of $ f(n) = n \cdot \left(1- \prod_{i=1}^n (1-\frac{1}{p_i})\right)$

Published on 23 Dec 2016 - 16:33

score 34 · Answer 5 · 2016-12-24 18:44:39

34

Views

sequence and product

Published on 24 Dec 2016 - 18:44

score 185 · Answer 6 · 2026-03-25 22:06:09

185

Views

Prove that:$(\phi-1)^1(2-\phi)^{1\over4}(2\phi-3)^{1\over9}(5-3\phi)^{1\over16}\cdots(F_{n+1}-\phi F_n)^{1\over n^2}=\phi^{-H_n}$

Published on 25 Mar 2026 - 22:06

score 186 · Answer 7 · 2026-03-28 07:59:33

186

Views

Euclidean geometry: Given two tangents $PM$, $PN$ to a circle with center $O$, find the value $QX\cdot RY$

Published on 28 Mar 2026 - 7:59

score 601 · Answer 8 · 2026-03-29 14:32:27

601

Views

Why is $\sup f_- (n) \inf f_+ (m) = \frac{5}{4} $?

Published on 29 Mar 2026 - 14:32

score 74 · Answer 9 · 2016-12-31 05:20:50

74

Views

Writing as a Product of $k$ factors

Published on 31 Dec 2016 - 5:20

score 753 · Answer 10 · 2016-12-31 07:12:48

753

Views

Proof without induction of the inequalities related to product $\prod\limits_{k=1}^n \frac{2k-1}{2k}$

Published on 31 Dec 2016 - 7:12

score 120 · Answer 11 · 2016-12-31 15:17:54

120

Views

Prove $0<a_k\in \mathbb R$ and $\prod\limits_{k=1}^n a_k =1$, then $\prod\limits_{k=1}^n (1+a_k) \ge 2^n$

Published on 31 Dec 2016 - 15:17

score 421 · Answer 12 · 2017-01-01 09:25:59

421

Views

Series representaion of $\frac {\pi}{\sin{\pi z}}$?

Published on 01 Jan 2017 - 9:25

score 165 · Answer 13 · 2017-01-02 07:01:01

165

Views

Products of $|q|<1$ : $\prod_{n=1}^{\infty}(1-q^n) = \prod_{n=1}^{\infty} (1-q^{2n})(1-q^{2n-1})$

Published on 02 Jan 2017 - 7:01

score 48 · Answer 14 · 2017-01-02 17:25:32

48

Views

What property is being used?

Published on 02 Jan 2017 - 17:25

score 100 · Answer 15 · 2017-01-03 05:54:26

100

Views

Show the identity: $\prod^{2n+1}\limits_{i=1}(x+n+1-i) = x\prod^{n}\limits_{i=1}(x^2-i^2)$

Published on 03 Jan 2017 - 5:54

List Question

Given that $G$ is subdirect product of $A$ and $B,$ and $G/G'$ is not subdirect product of $A/A'$ and $ B/B',$ this group contains $G'$?

Does this limit with a Product Exist?

About $\prod_{n\in\mathbb Z}\left[{\tanh\Big(\frac{\pi}{2}\sqrt{a^2n^2+ab}\Big)\over\tanh\Big(\frac{\pi}{2}\sqrt{n^2/a^2+b/a}\Big)}\right]^{(-1)^n}=1$

Derivative of $ f(n) = n \cdot \left(1- \prod_{i=1}^n (1-\frac{1}{p_i})\right)$

sequence and product

Prove that:$(\phi-1)^1(2-\phi)^{1\over4}(2\phi-3)^{1\over9}(5-3\phi)^{1\over16}\cdots(F_{n+1}-\phi F_n)^{1\over n^2}=\phi^{-H_n}$

Euclidean geometry: Given two tangents $PM$, $PN$ to a circle with center $O$, find the value $QX\cdot RY$

Why is $\sup f_- (n) \inf f_+ (m) = \frac{5}{4} $?

Writing as a Product of $k$ factors

Proof without induction of the inequalities related to product $\prod\limits_{k=1}^n \frac{2k-1}{2k}$

Prove $0<a_k\in \mathbb R$ and $\prod\limits_{k=1}^n a_k =1$, then $\prod\limits_{k=1}^n (1+a_k) \ge 2^n$

Series representaion of $\frac {\pi}{\sin{\pi z}}$?

Products of $|q|<1$ : $\prod_{n=1}^{\infty}(1-q^n) = \prod_{n=1}^{\infty} (1-q^{2n})(1-q^{2n-1})$

What property is being used?

Show the identity: $\prod^{2n+1}\limits_{i=1}(x+n+1-i) = x\prod^{n}\limits_{i=1}(x^2-i^2)$

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