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Recent questions tagged group-theory

1 votes
2 answers
95
NIELIT 2022 April Scientist B | Section B | Question: 65
Let $\text{G}$ be a multiplicative group and $a \in \text{G.}$ If the order of $a$ is $6,$ then the order of $a^{5}$ is equal to : $1$ $5$ $6$ $30$
Let $\text{G}$ be a multiplicative group and $a \in \text{G.}$ If the order of $a$ is $6,$ then the order of $a^{5}$ is equal to :$1$$5$$6$$30$
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0 votes
1 answer
97
made easy test series - group theory
Let G be a group of 52 elements. The largest possible size of a subgroup of G other than G itself is ____.
Let G be a group of 52 elements. The largest possible size of a subgroup of G other than G itself is ____.
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3 votes
1 answer
100
NIELIT 2016 DEC Scientist B (CS) - Section B: 28
Which one of the following is NOT necessarily a property of a Group? Commutativity Associativity Existence of inverse for every element Existence of identity
Which one of the following is NOT necessarily a property of a Group?CommutativityAssociativityExistence of inverse for every elementExistence of identity
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4 votes
5 answers
101
NIELIT 2017 DEC Scientist B - Section B: 48
On a set $A = \{a,b,c,d\}$ a binary operation $*$ ... The relation is Commutative but not associative Neither commutative nor associative Both commutative and associative Associative but not commutative
On a set $A = \{a,b,c,d\}$ a binary operation $*$ is defined as given in the following table.$$\begin{array}{|c|cccc|}\hline\text{*}&a&b&c&d\\\hline \text{a}&a&c&b&d\\\te...
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