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Deepak Patra posted an Question
December 27, 2021 • 11:20 am 30 points
  • IIT JAM
  • Mathematics (MA)

Is it a true statement?????????????if h and h, ate subgroups ofa group g then h,h, = {hh e gh e h, h e h,} isasubgroup ofg. itifr-2012]

is it a true statement?????????????if H and H, ate subgroups ofa group G then H,H, = {hh e Gh e H, h e H,} isasubgroup ofG. ITIFR-2012]

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  • Anuj s.

    In general, the product of two subgroups S and T is a subgroup if and only if ST = TS, and the two subgroups are said to permute. (Walter Ledermann has called this fact the Product Theorem, but this name, just like "Frobenius product" is by no means standard.)

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    Deepak patra

    that means in case of non abelian group G the result fails ???. here the statement is true or false????

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    false

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    ma'am is there any group which is finite but its subgroups are infinite???

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    no bcz o(H)

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    maam this statement is true or false???

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    yes (z+) countable group (mz, +) countable subgroups

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    but ma'am ans given is false .... Q/Z is finite group but its subgroup are infinite ... i think so????

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    Q/Z not finite

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    z+1/n n€N infinite coset

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    then how the result given is false???

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