Teaching DSSSB TGT Mock Test 2025 Mathematical Science Algebra Group & Subgroups

Which statement is not correct when H acts on G by left multiplication?

1
there are no fixed points ( if H ≠ G).
2
staba = { h :ha = a } = {e} is trivial. 
3
the orbits are the right H - cosets.
4
there are no fixed points {if [H] > 1} 
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