in Set Theory & Algebra recategorized by
6,567 views
36 votes
36 votes
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________.
in Set Theory & Algebra recategorized by
6.6k views

1 Answer

81 votes
81 votes
Best answer

Lagrange's theorem: For any finite group $G,$ the order (number of elements) of every subgroup $L$ of $G$ divides the order of $G.$
$G$ has $15$ elements.
Factors of $15$ are $1,3,5,$ and $15.$
Since, the given size of $L$ is at least $4$ $(1$ and $3$ eliminated$)$ and not equal to $G(15$ eliminated$),$ the only size left is  $5.$

Size of $L$ is $5.$

edited by

2 Comments

WHT IF A GROUP  IS AN INFINITE GROUP??
0
0
concept of order exists fpr finite groups only
17
17
Answer:

Related questions