Instead of use another widget I wish to code the technique to incorporate the Wordpress "Groups" widget directly inside the content of the page or publish. Any ideas?
I believe, you look for this.
http://wordpress.stackexchange.com/questions/36511/are-widgets-meant-to-be-used-outside-of-sidebars
To include wordpress publish groups in to the template file you should utilize
<?php wp_list_categories($args); ?>
Default arguments are :
<?php $args = array(
'show_option_all' => ,
'orderby' => 'name',
'order' => 'ASC',
'show_last_update' => 0,
'style' => 'list',
'show_count' => 0,
'hide_empty' => 1,
'use_desc_for_title' => 1,
'child_of' => 0,
'feed' => ,
'feed_type' => ,
'feed_image' => ,
'exclude' => ,
'exclude_tree' => ,
'include' => ,
'hierarchical' => true,
'title_li' => __( 'Categories' ),
'show_option_none' => __('No categories'),
'number' => NULL,
'echo' => 1,
'depth' => 0,
'current_category' => 0,
'pad_counts' => 0,
'taxonomy' => 'category',
'walker' => 'Walker_Category' );
?>
or simply employ it without parameters, for the reason that situation defaults works.
<?php wp_list_categories(); ?>
read much more about this function here