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GATE19879f
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Give the composition tables (Cayley Tables) of the two non isomorphic groups of order 4 with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.
gate1987
groupisomorphism
settheory&algebra
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Nov 15, 2016
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Set Theory & Algebra
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makhdoom ghaya
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TIFR2014MathsB5
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 $\mathbb{Z}/4$
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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 $\mathbb{Z}/4$
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Dec 17, 2015
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TIFR2015MathsA4
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. $S = \infty$
asked
Dec 19, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
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75
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tifrmaths2015
groups
groupisomorphism
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TIFR2011MathsB7
There is a nontrivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
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160
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tifrmaths2011
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TIFR2011MathsB3
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.
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Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
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88
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tifrmaths2011
groups
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+7
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6
GATE19879e
How many true inclusion relations are there of the from $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
asked
Nov 15, 2016
in
Set Theory & Algebra
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makhdoom ghaya
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gate1987
settheory&algebra
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+13
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2
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7
GATE19879b
How many onetoone functions are there from a set $A$ with $n$ elements onto itself?
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Nov 15, 2016
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Set Theory & Algebra
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makhdoom ghaya
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730
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gate1987
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