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If G G " id="MathJax-Element-64-Frame" role="presentation" style="position: relative;" tabindex="0"> G G G G G is abelian, then " id="MathJax-Element-65-Frame" role="presentation" style="position: relative;" tabindex="0"> G is a union of its proper subgroups.

If " id="MathJax-Element-66-Frame" role="presentation" style="position: relative;" tabindex="0"> G has a normal subgroup " id="MathJax-Element-67-Frame" role="presentation" style="position: relative;" tabindex="0"> N of prime order, then " id="MathJax-Element-68-Frame" role="presentation" style="position: relative;" tabindex="0"> G is cyclic.

G is a union of proper subgroups if and only if G G " id="MathJax-Element-69-Frame" role="presentation" style="position: relative;" tabindex="0"> G G G G G is not simple.

Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Algebra Group & Subgroups

G $G$ be any finite group. Which one of the following is necessarily true?

$G$ has an element of order equal to the least common multiple of the orders of all elements.

G

is abelian, then

is a union of its proper subgroups.

has a normal subgroup

of prime order, then

is cyclic.

G

is a union of proper subgroups if and only if

G

is not simple.

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G $G$ be any finite group. Which one of the following is necessarily true?

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