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Recent questions tagged group-isomorphism

2 votes
2 answers
2
Non isomorphic group of order 10
Number of non isomorphic group of order 10
Number of non isomorphic group of order 10
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2 votes
1 answer
4
TIFR-2015-Maths-A-4
Let $S$ be the collection of (isomorphism classes of) groups $G$ which have the property that every element of $G$ commutes only with the identity element and itself. Then $|S| = 1$ $|S| = 2$ $|S| \geq 3$ and is finite $|S| = \infty$
Let $S$ be the collection of (isomorphism classes of) groups $G$ which have the property that every element of $G$ commutes only with the identity element and itself. The...
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1 votes
0 answers
5
TIFR-2014-Maths-B-5
Which of the following groups are isomorphic? $\mathbb{R}$ and $C$ $\mathbb{R}^{*}$ and $C^{*}$ $S_{3}\times \mathbb{Z}/4$ and $S_{4}$ $\mathbb{Z}/2\times \mathbb{Z}/2$ and $\mathbb{Z}/4$
Which of the following groups are isomorphic? $\mathbb{R}$ and $C$ $\mathbb{R}^{*}$ and $C^{*}$ $S_{3}\times \mathbb{Z}/4$ and $S_{4}$ $\mathbb{Z}/2\times \mathbb{Z}/2$ a...
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1 votes
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6
TIFR-2014-Maths-B-3
Let $S_{n}$ be the symmetric group of $n$ letters. There exists an onto group homomorphism From $S_{5}$ to $S_{4}$ From $S_{4}$ to $S_{2}$ From $S_{5}$ to $\mathbb{Z}/5$ From $S_{4}$ to $\mathbb{Z}/4$
Let $S_{n}$ be the symmetric group of $n$ letters. There exists an onto group homomorphism From $S_{5}$ to $S_{4}$ From $S_{4}$ to $S_{2}$ From $S_{5}$ to $\mathbb{Z}/5$F...
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2 votes
0 answers
7
TIFR-2011-Maths-B-7
There is a non-trivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.
There is a non-trivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.
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1 votes
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8
TIFR-2011-Maths-B-3
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.
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2 votes
1 answer
9
TIFR-2011-Maths-A-22
There exists a group with a proper subgroup isomorphic to itself.
There exists a group with a proper subgroup isomorphic to itself.
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