latter are the so called $A$-groups, [@taunt]).

\[MainResult\] Let $n>1$ be an integer. Let $p_{1}, p_{2}, \dots, p_{n}$ be distinct primes. There exist positive integers $l_1, l_2, \dots,
l_n$, only depending on $p_{1},p_{2}, \dots , p_n$, such that for each $n$-tuple of integers $m_1\geq l_1$, $m_2 \geq l_2, \dots
,m_n\geq l_n$ there exists a simple left brace of order $p_{1}^{m_1}p_{2}^{m_2}\cdots p_n^{m_{n}}$ that has a metabelian multiplicative group with abelian Sylow subgroups.

The paper is organized as follows. We start in Section 2 with correcting the proof of a result from [@BDG2], saying that every finite solvable $A$-group $(B,\cdot)$ admits a structure of a left brace. We also discuss the structure of finite left braces of this type, based on the structure of $A$-groups [@hall; @taunt]. Then a very general new construction of left braces of the latter type is presented. These braces $(B,+,\cdot)$ have the additional property that the multiplicative group $(B, \cdot)$ is metabelian. In Section 3 we construct a new family of finite simple left braces. This relies on concrete classes of braces presented in Section 2. Consequently, the main result of the paper, Theorem \[MainResult\], is proved. Our construction requires special elements of the Sylow $p$-subgroups of 