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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.)

• ##### Deepak patra

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

false

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

no bcz o(H)

maam this statement is true or false???

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

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

Q/Z not finite

z+1/n n€N infinite coset

then how the result given is false???

• ##### Ishu 1

products of two subgroups is subgroup if H1H2=H2H1

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