"If H and K are subgroups of G,..." was answered by students like you

pimpinan15t

Answered question

2022-02-14

If H and K are subgroups of G,

| H | = 20 and | K | = 32

then a possible value of

| H \cap K |

is
1) 2
2) 8
3) 6
4) 16

Anahi Pearson

Beginner2022-02-15Added 16 answers

Order of

H \cap K

must divide order of H and order of K
i.e.,

| H \cap K |

must divide |H| and |K|.
If

| H \cap K | = 8

, 8 divides 32 which is |K| but 8 does not divide

20 = | H |

.
Hence

| H \cap K | \neq 8

.
If

| H \cap K | = 6

, 6 does not divide

32 = | K |

and 6 does not divide

20 = | H |

.
Hence

| H \cap K | \neq 6

.
If

| H \cap K | = 16

, 16 divides

32 = | K |

but 16 does not divides

20 = | H |

.
Hence

| H \cap K | \neq 16

| H \cap K | = 2

. 2 divides

32 = | K |

and 2 divides

20 = | H |

.
Hence

| H \cap K | = 2

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