XSLT to print values of a node based on its position repeatively

I have to transform this sample xml in xslt 1.0 or xslt 2.0 Source XML

<root>
    <group>
        <spec>
            <name>AAA1</name>
        </spec>
        <spec>
            <name>AAA2</name>
        </spec>
        <spec>
            <name>AAA3</name>
       </spec>
    </group>
 <group>
        <spec>
            <name>BB1</name>
        </spec>
        <spec>
            <name>BB2</name>
        </spec>
        <spec>
            <name>BB3</name>
       </spec>
    </group>
</root>

Required XML OUTPUT

<?xml version="1.0" encoding="UTF-8"?>
<root>
  <group>AAA1|BB1|AAA2|BB2|AAA3|BB3</group>
</root>

I tried the following xslt:

XSLT

    <xsl:stylesheet version="1.0" xmlns:xsl="http://ift.tt/tCZ8VR">
    <xsl:output method="xml" indent="yes" />
    <xsl:template match="root">
    <root>
      <group>
       <xsl:for-each select="group">
          <xsl:for-each select="spec">
            <xsl:choose>
            <xsl:when test="position() != last()">
            <xsl:value-of select="name" /><xsl:text>|</xsl:text>
            </xsl:when>
            <xsl:otherwise>
               <xsl:value-of select="name" />
            </xsl:otherwise>
             </xsl:choose> 
          </xsl:for-each>
       </xsl:for-each>
       </group>
    </root>
</xsl:template>
</xsl:stylesheet>

Current-output

<?xml version="1.0" encoding="UTF-8"?>
<root>
<group>AAA1|AAA2|AAA3BB1|BB2|BB3</group>
</root>

How can I do this? Should I create a template a call it recursively?